Questions on Geometry: Pythagorean theorem answered by real tutors!

Tutors Answer Your Questions about Pythagorean-theorem (FREE)

Question 571129: The measures of the legs of angle ABC are 5 and 8. Find the length of the hypotenuse. Show diagram and calculation. Simplify your answer.
Answer by richard1234(4794)

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Pythagorean theorem

Question 571131: The hypotenuse of angle XYZ is 10 and length of one of its legs is 8. Find the length of the other leg. Show diagram and calculation.
Answer by mananth(10549)

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Pythagoras theorem
Hypotenuse ^2 = leg1^2+leg2^2
Leg1^2= Hypotenuse^2-leg2^2
Hypotenuse = 10 ft
leg1= 8 ft
leg2= ? ft
Leg1^2= Hypotenuse^2-leg2^2
leg1^2= 10 ^2 - 8 ^2

leg1= sqrt%0936%09

leg1= 6 ft

Question 571125: Name three(3) sets of Pythagorean triplets and prove that they are indeed Pythagorean triplets.
Answer by mananth(10549)

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There are many many triplets
PYthagoras theorem states

the sum of squares of the adjacent sides = hypotenuse^2
leg1^2+leg2^2=hypotenuse^2
In a right triangle the largest side is aways the hypotenuse.
First the basic one
3,4,5
3^2+4^2=5^2
(+16=25
25=25
----
5,12,13
5^2+12^2=13^2
25+144=169
169=169
-------------
Third one you can find

Question 570686: If a square has a diagonal of 40 inches how long is each side of the square
Answer by stanbon(48535)

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If a square has a diagonal of 40 inches how long is each side of the square
----
Let each of the sides of the square be "x":
Equation:
x^2 + x^2 = 40^2
------
2x^2 = 1600
x^2 = 800
x^2 = 400*2
x = 20*sqrt(2)
-----
Cheers,
Stan H.
=============

Question 570395: a square garden has a side length of 10 meters. What is the length of the diagonal of the garden , to the nearest hundredth ?

Answer by solver91311(12126)

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The diagonal of any square of side measure

measures exactly

. Do the arithmetic and round to your heart's content.

John

My calculator said it, I believe it, that settles it

The Out Campaign: Scarlet Letter of Atheism

Question 570213: The foot of a ladder is placed 12 feet from a wall. If the top of the ladder rests 9 feet up on the wall, how long is the ladder?
Answer by nerdybill(5404)

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The foot of a ladder is placed 12 feet from a wall. If the top of the ladder rests 9 feet up on the wall, how long is the ladder?
.
Apply Pythagorean theorem:
Let x = length of ladder
then
9^2 + 12^2 = x^2
81 + 144 = x^2
225 = x^2
15 feet = x

Question 568719: What to do when both legs are x?

Found 2 solutions by sEahors3, Alan3354:
Answer by sEahors3(4)   (Show Source):
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i guess the formula will be
2(x^2) = h^2
explanation :
x^2 + y^2 = h^2
both legs are x
so y = x
x^2 + x^2 = h^2
2(x^2) = h^2
=) hope this helps

Answer by Alan3354(21583)   (Show Source):
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What to do when both legs are x?
-------------
What are you asked to do?

Question 568656: (Pythogorean Theorem) The foot of a ladder is placed 6 feet from a wall. If the top of the ladder rests 8 feet up on the wall, how long is the ladder?
Answer by stanbon(48535)   (Show Source):
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The foot of a ladder is placed 6 feet from a wall. If the top of the ladder rests 8 feet up on the wall, how long is the ladder?
-------
Draw the picture:
base = 6
height = 8
hypotenuse = ladder = x
------
x^2 = 6^2 + 8^2
x^2 = 36 + 64
x = sqrt(100)
x = 10 ft.
Cheers,
Stan H.

Question 568107: It is my 2nd day in my geometry class, I have switched from an online school & I have an upcoming test on slope/midpoint/distance. Im stuck on a question from the study guide because I was not there for the lessons. I need help ASAP!
The question is:
The length of a rectangle is three times as long as it is wide. If the length of the diagonal is 10sqrt6 feet, find the area of the rectangle.
I cannot solve for this question no matter what I try!
Answer by scott8148(5880)   (Show Source):
You can put this solution on YOUR website!
if x is the width, then 3x is the length

by Pythagoras ___ x^2 + (3x)^2 = [10sqrt(6)]^2 ___ x^2 + 9x^2 = 10^2 * [sqrt(6)]^2

10x^2 = 600 ___ x^2 = 60

the area is ___ x * 3x ___ or 3x^2

3(60) = 180

Question 566007: a squared = (x+3)
b squared = 4(x+2)
c squared = 625
I have got to:
xsq+6x+9+4xsq+16x+16=625
then get stuck
Answer by stanbon(48535)   (Show Source):
You can put this solution on YOUR website!
a squared = (x+3)
b squared = 4(x+2)
c squared = 625
----
Pythagoras:
a^2 + b^2 = c^2
x+3+4x+8 = 625
5x+11 = 625
5x = 614
x = 122.8
==============
Cheers,
Stan H.
==============

Question 565887: if i have a right triangle where 26 is the hypotenuse(C) and bottom leg is 21 (C). how do i find A, the side leg?
Answer by stanbon(48535)   (Show Source):
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if i have a right triangle where 26 is the hypotenuse(C)
and bottom leg is 21 (C).
how do i find A, the side leg?
-------
Pythagoras:
21^2 + A^2 = 26^2
---
A^2 = 26^2 - 21^2
----
A^2 = 235
---
A = 15.33
================
Cheers,
Stan H.

Question 565683: What do i do if ther are Square Roots? Like this problem: a=5, b=?, and c= sqaure root of 89? I have to find the missimg length!
Answer by Leaf W.(83)   (Show Source):
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Just do the same thing as you would normally do. When you square a square root of a number, it cancels out to just the number--if you square the square root of x, the result is x.
a = 5, b = ?, c =

x = 8
Therefore, b = 8.
Hope I helped! Good luck! =)

Question 565556: one adjacent is 12cm, the other is x. The hypotenuse is x+8. What is x? I can work it out by trial and error and get the answer 5, but how do I get it using algebra?
Answer by stanbon(48535)   (Show Source):
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one adjacent is 12cm, the other is x. The hypotenuse is x+8. What is x?
----------------
Equation:
(x+8)^2 = 12^2 + x^2
-----
x^2 + 16x + 64 = 144 + x^2
16x = 80
x = 5
=================
Cheers,
Stan H.
=================

Question 565496: Find the missing lengths in each of these triangles. You must express your answers in radical form
Answer by Alan3354(21583)   (Show Source):
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What triangles?

Question 565306: using pythagorean theorem:
how do i solve using a square root as one of the sides?
for example: a^2=26 b^2=(square root 596) c^2=?

Answer by Theo(2967)   (Show Source):
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the square root of 596 squared is equal to 596.
the square root of anything squared is anything.
example:
the square root of 4^2 = 4
the square root of 6^2 = 6
you can prove this for yourself by squaring 4 and squaring 6
you get 16 and 36
square root of 16 = 4
square root of 36 = 6
in your problem you want to take the square root of 596^2.
that equals 596.
if you use your calculator and square 596 you'll get 355216
if you use your calculator and take the square root of 355216 you'll get 596.

Question 563564: Diagonals of a rhombus are of lengths 16cm and 12cm.find the length of it's sides
Answer by Theo(2967)   (Show Source):
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all sides of a rhombus are equal in length.
the diagonals of the rhombus intersect at a 90 degree angle.
the diagonals and the sides of the rhombus form right triangles.
one leg of these right triangles is equal to 8 cm in length.
the other leg of these right triangles is equal to 6 cm in length
that would be half the length of each diagonal.
the sides of the triangle form the hypotenuse of these right triangles.
the formula is:
hypotenuse squared = one leg squared plus other leg squared.
this makes the hypotenuse squared equal to 8^2 + 6^2 = 64 + 36 = 100
the hypotenuse is the square root of 100 which makes the hypotenuse equal to 10.
the sides of the rhombus are equal to 10 cm.

Question 562913: I have a question. what do you do if you need to prove a triangle is a right triangle, but you only have variable coordinates for that triangle. Here's what I have so far: Triangle ABC: A(x,0); B(x,y); C(2x,0)
Finding AB:

Finding BC:

Finding AC:

Final Steps: a^2+b^2=c^2

I'm confused on what to do next. I know that if a^2+b^2=c^2 then it is a right triangle. But, I can't solve it any furthur. I also can't use sin, cos, or tan. Thannk you in advance.

Answer by mananth(10549)   (Show Source):
You can put this solution on YOUR website!
Triangle ABC: A(x,0); B(x,y); C(2x,0)
Finding AB:

=y
Finding BC:

Finding AC:

=x
Final Steps: a^2+b^2=c^2

m.ananth@hotmail.ca

Question 562716: I've been stuck on this problem for a long time, and I REALLY need some help!
The question is:
"The longer leg of a right triangle is 4 feet longer than the other leg. Find the length of the two legs if the hypotenuse is 20 feet." I know that you set it up like this: x^2+(x+4)^2=20.
I need to show work, but I don't really know what I'm doing.
Answer by issacodegard(60)   (Show Source):
You can put this solution on YOUR website!
Hi, your right about how to set it up! So I'll work out the steps,

Expand using FOIL:

Simplify:

Use the quadratic formula:

Since x represents a distance, we know x>=0. So, the length of the first leg is

And, the second leg has length,

Question 562396: do 26,24,10 make up an right angle?
Answer by fcabanski(385)   (Show Source):
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Yes, those side lengths are a right triangle. The sum of the squares of the smaller sides equal the square of the larger side.

10^2 + 24^2 = 26^2

If you need help understanding math so you can solve these problems yourself, then one on one online tutoring is the answer ($30/hr). If you need faster solutions with guaranteed detailed answers, then go with personal problem solving ($3.50-$5.50 per problem). Contact me at fcabanski@hotmail.com

Question 562266: Y^2=x^2+12^2 represents the Pythagorean Theorem for a right triangle, where one of the shorter sides is 12 feet long, the other side is x(in feet), and y is the hypottenuse of the triangle.
Graph the equation using at least 5 to 8 points.
thank you
Rod Curley
Answer by ankor@dixie-net.com(12692)   (Show Source):
You can put this solution on YOUR website!
Y^2=x^2+12^2 represents the Pythagorean Theorem for a right triangle, where one of the shorter sides is 12 feet long, the other side is x(in feet), and y is the hypotenuse of the triangle.
Graph the equation using at least 5 to 8 points.
:
y^2 = x^2 + 12^2
Find the square root of both sides, we need this form to graph it
y =
:
Plot 6 points from 2 to 16
x = 2;
y =
y =
y = 12.2
:
x = 3.5
y =
y =
y =
y = 12.5
:
x = 5
y =
y =
y =
y = 13
:
Construct a table, you can complete it, the same way we did the first 3 values:
x | y
-------
2 |12.2
3.5|12.5
5 |13.0
9 |
12 |
16 |
:
Your graph should be similar to this:

You have one leg on the horizontal, x; and the hypotenuse on the vertical, y

Question 561713: The perimeter of a triangle is the "distance around the outside". If you have a triangle whose sides are a, b, and c, then the perimeter is a+b+c. Your peice of property is a triangle, which is bordered by three square peices of property. The first square (the hypotenuse) has and area of 200 square miles. The second square (side a) has an area of 50 square miles. The third square (side b) has an area of 72 square miles. What is the perimeter of your property?
(HINT: after you simplify your answer, it will be in the form a√b where a is a 2-digit number and b is a one-digit number.)
Please help me figure this out!
Answer by ankor@dixie-net.com(12692)   (Show Source):
You can put this solution on YOUR website!
The perimeter of a triangle is the "distance around the outside".
If you have a triangle whose sides are a, b, and c, then the perimeter is a+b+c.
Your piece of property is a triangle, which is bordered by three square piece of property.
The first square (the hypotenuse) has and area of 200 square miles.
The second square (side a) has an area of 50 square miles.
The third square (side b) has an area of 72 square miles.
What is the perimeter of your property?
:
Draw a picture of this and it will make sense to you.
Each side of the triangle is the square root of the square on the that side, so you have:
:
P =
:
Factor these values inside to reveal some perfect squares:
P =
;
Extract the square root of these perfect squares
P =
;
note they are all like terms, we can just add them up
p =

Question 561661: how to derive the pythagorean theorem?
Answer by richard1234(4794)   (Show Source):
You can put this solution on YOUR website!
There are several proofs of the Pythagorean theorem; the one I know best involves partitioning a square of side length a+b into four right triangles with legs a, b and hypotenuse c. Using the diagram, you can prove that a^2 + b^2 = c^2.

http://en.wikipedia.org/wiki/Pythagorean_theorem

Question 560576: please help me to solve this questions; if the scale distance on a map varies directly as the actual distance.if the actual distance represented by 1
cm is 10km what is the actual distance corresponding to 84cm?

Answer by josmiceli(6784)   (Show Source):
You can put this solution on YOUR website!
Use the ratio:
( cm/km = cm/km )
Multiply both sides y
km
The actual distance is 840 km

Question 560568: please help me to solve this:if the hypotenuse of an isosceles rigt triangle 18 squre of 2cm.find lenght of the other sides(hint:use pythagoren theorem
Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!
If the hypotenuse of a isosceles right triangle is h and x are the legs, then

So in this case, and

So this means that . I'll let you finish and solve for x.
-------------------------------------------------------------------------------------------------
If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
-------------------------------------------------------------------------------------------------

Question 559794: A forty foot ladder is set against the wall. the distance of the base of the ladder to the wall is equal to the height of the ladder. How high is the ladder on the wall?
If I was to use the theorem, my answer is 0. (40)^2-(40)^2=b^2 1600-1600=b^2
0=b^2.
On the drawing it shows a 90o angle between the ladder and the wall.
Answer by mananth(10549)   (Show Source):
You can put this solution on YOUR website!
let distance of foot of ladder be x
height will also be x
ladder length = 40
The ladder ,ground and the wall form a right triangle
ground distance = leg2
height at which ladder touches
Hypotenuse = ladder length
Pythagoras theorem states that

Hypotenuse ^2= leg1^2+leg2^2
40^2=x^2+x^2
1600=2x^2
1600/2= x^2
800=x^2
take the square root
x=28.285 feet

Question 559439: can you find the distance between the following points using the Pythagorean theorem: (-4, -9), (-11, -9)
Answer by mananth(10549)   (Show Source):
You can put this solution on YOUR website!
Distance between two points
x1 y1 x2 y2
d=
-4 -9 -11 -9
d=
d=
d=
d= 7.00

Question 559122: two angles of a right triangle are complementary and are in the ratio of 1:2 What are the measures of the three angles?
Answer by josmiceli(6784)   (Show Source):
You can put this solution on YOUR website!
The 3 angles must add up to 180 degrees in
any triangle.
It is a right triangle, so 1 of the angles is 90 degrees
Call the other 2 angles and

(1)
--------------
given:

Multiply both sides by
(2)
Substitute (2) into (1)
(1)
(1)
(1)
and, since
(1)
(1)
(1)
The angles are 90, 60, and 30

Question 557663: "Do the lengths of the three sides of an isosceles triangle always, sometimes, or never satisfy the Pythagorean theorem"
Answer by richard1234(4794)   (Show Source):
You can put this solution on YOUR website!
Sometimes, only if you have a right isosceles triangle (45-45-90 triangle).

Question 557602: Televisions are sold by the length of the diagonal across the screen. If a new 48-in television screen is 42 in. wide, how tall is the screen to the nearest inch?
Answer by rfer(10417)   (Show Source):
You can put this solution on YOUR website!
42^2+x^2=48^2
1764+x^2=2304
x^2=2304-1764
x^2=540
x=23.24

Question 557594: right triangles ABC has legs of lengths 4 ft and 7 ft. what is the length of the triangle's hypotenuse?
Answer by neatmath(225)   (Show Source):
You can put this solution on YOUR website!

We can go directly to the Pythagorean Theorem on this one:

where a and b are the legs of the triangle, and c is the hyptotenuse of the triangle.

Given legs of 4 ft and 7 ft, we have:

or

Since we are talking about distances, we can ignore the negative solution.

Thus, our anwer is:

The length of the hypotenuse is exactly ft long.

This is approximately 8.06 ft, which makes sense given our triangle.

I hope this helps! :)

*******************************************************

Email Scott King: neatmath@yahoo.com for help with specific problems,

or to inquire about low-cost mathematics tutoring via email or other methods.

Paypal is always accepted for detailed assistance with single problems.

Single problems would range from 50 cents to 5 dollars each, depending on their complexity.

Question 557587: a square has side length 9 in, what is the lenght of the longest line segment that can be drawn between any two points of the square?
Answer by neatmath(225)   (Show Source):
You can put this solution on YOUR website!

The longest line segment that can be drawn from any 2 points on a square,

must naturally be a diagonal of a square. No other possible line segment will be as long as any diagonal of the square.

You can test this out with any ruler, and any true square.

So, given a side of 9 cm, we can use the Pythagorean Theorem to find the length of the diagonal of the square.

or

Since we are dealing with distances, we can discard the negative solution.

which is the exact answer

The longest line segment would be cm.

Alternatively, we can find an approximation for this answer:

cm

Using the familiar rules of geometry, and recognizing that a square is cut into two 45-45-90 triangles by a diagonal,

we could have immediately determined the length of the diagonal to be cm long.

But then we wouldn't have had the nice opportunity to use the Pythagorean Theorem!

I hope this helps! :)

*******************************************************

Email Scott King: neatmath@yahoo.com for help with specific problems,

or to inquire about low-cost mathematics tutoring via email or other methods.

Paypal is always accepted for detailed assistance with single problems.

Single problems would range from 50 cents to 5 dollars each, depending on their complexity.

Question 557505: How do key into the calculator square root 180 when using the Pythagorean Theoran
Answer by stanbon(48535)   (Show Source):
You can put this solution on YOUR website!
How do key into the calculator square root 180 when
using the Pythagorean Theorem
---
If you have a TI calculator:
2nd then x^2 button
key in 180
ENTER to get 13.4164..
Cheers,
Stan H.
=======================

Question 557314: is pythagorean theorem a square + b square = c square
Found 2 solutions by AnlytcPhil, richard1234:
Answer by AnlytcPhil(1116)   (Show Source):
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That is true if, but only if, you label the measure of the hypotenuse of a right triangle "c" and the measures of the legs of the right triangle "a" and "b". That is the usual way of labeling. The Pythagorean theorem stated in words is In a right triangle the square of the measure of the side opposite the right angle equals the sum of the squares of the measures of the sides that make the right angle. Edwin

Answer by richard1234(4794)   (Show Source):
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Yes, as long as a and b are the shorter two sides and c is the hypotenuse of a right triangle.

Question 556923: Using the Pythagorean Theorem, find the length of a leg of a right triangle if the other leg is 8 feet long and the hypotenuse is 10 feet long.
Found 2 solutions by JBarnum, Alan3354:
Answer by JBarnum(1826)   (Show Source):
You can put this solution on YOUR website!

a=8 c=10 find b

Answer by Alan3354(21583)   (Show Source):
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Using the Pythagorean Theorem, find the length of a leg of a right triangle if the other leg is 8 feet long and the hypotenuse is 10 feet long.
-----------
Do that.

Question 556837: beginning with a 3 dimentional rectangular box, how is the degree of the angle of turn determined where a line enters the box and then proceeds to the furthest corner within the box

Answer by stanbon(48535)   (Show Source):
You can put this solution on YOUR website!
What are the dimensions of the box
and what angle are you trying to size?
Cheers,
Stan H.

Question 556498: Using the pythagorean Theorem, find the hypotenuse of a right triangle whose legs are 8 and 15
Answer by prateekagrawal(47)   (Show Source):
You can put this solution on YOUR website!
(h)^2 = a^2 +b^2
here: a=8 and b=5
so,
h^2 = 8^2 + 15^2
h^2 = 64 + 225
h^2 = 289.
h^2 =17^2
h=17.
so, 17 is the hypotenuse.

Question 556227: if (a)is the length of a leg of a triangle, then (a) is less than the length of the hypotenuse. true or false
Answer by Theo(2967)   (Show Source):
You can put this solution on YOUR website!
true.
the hypotenuse of a right triangle is longer than either of the other 2 legs of the triangle.
it would have to be a right triangle since hypotenuse doesn't apply to any triangle other than a right triangle.

Question 556184: i badly needed your precious help, please i think i'm going to die. my problem is the school stage is rectangular in shape. its diagonal is 13 m. the length is 7m longer than its width. find the length and width of the stage.. please i really need your answer
Answer by Theo(2967)   (Show Source):
You can put this solution on YOUR website!
diagonal is 13 meters.
length is 7 meters longer than than the width.
let x = width.
this makes the length x + 7
diagonal and the length of the stage and the width of the stage form a right triangle whose hypotenuse is 13 meters in length.
using formula by pythagorus, we get:
hypotenuse squared = length squared plus width squared.
this becomes:
13^2 = (x+7)^2 + x^2 which becomes:
169 = x^2 + 14x + 49 + x^2 which becomes:
169 = 2x^2 + 14x + 49
subtract 169 from both sides of this equation to get:
2x^2 + 14x + 49 - 169 = 0
combine like terms to get:
2x^2 + 14x - 120 = 0
divide both sides of this equation by 2 to get:
x^2 + 7x - 60 = 0
factor this quadratic equation to get:
(x-5) * (x+12) = 0
solve for x to get:
x = -12 or x = 5
x can't be negative so your answer has to be:
x = 5
that means the width of the stage is 5 meters.
it also means that the length of the stage is 12 meters.
using pythagorus relationship, we get:
13^2 = 5^2 + 12^2 = 25 + 144 = 169
this confirms the values for the length and width of the stage are good.
the following diagram shows you what i mean:

Question 555793: Caroline and Trevor are flying a kite. Caroline is holding the kite and has let out 80 feet of kite string. Trevor is standing 25 feet from Caroline and is directly under the kite. Caroline is holding the string 3 feet above the ground. How far above the ground is the kite?
Answer by richwmiller(7655)   (Show Source):
You can put this solution on YOUR website!
80^2=25^2+(x)^2
6400=625+x^2
x=75.9934
add 3 feet
x+3=78.9934
about 79 feet above the ground

Question 554914: the area of a square is 81 square centimeters, find the length of the diagonal.
Found 2 solutions by MathTherapy, nyc_function:
Answer by MathTherapy(639)   (Show Source):
You can put this solution on YOUR website!

the area of a square is 81 square centimeters, find the length of the diagonal.

The diagonal of the square will form two 45-45 right triangles

In any 45-45 right triangle (isosceles right triangle), the hypotenuse equals one side, times square root of 2 (radical 2). Since one side = 9, then the length of the hypotenuse or the length of the diagonal can be written as:

Send comments and “thank-yous” to “D” at MathMadEzy@aol.com

Answer by nyc_function(2626)   (Show Source):
You can put this solution on YOUR website!
The area of a square = side times side.

In short, A = s times s or s^2

81 = s^2

Taking the square root of both sides, we get s = 9cm.

To find the diagonal, we use the Pathygorean Theorem.
Let d = the diagonal representing the hypotenuse of the right triangle formed by two sides of the square and the diagonal.

(side)^2 + (side)^2 = (diagonal)^2

9^2 + 9^2 = d^2

81 + 81 = d^2

162 = d^2

Taking the square root of both sides, we get d = sqrt{162}.

The length of the diagonal is the square root of 162
written as sqrt{162}.

Question 554848: If the side of a triangle are 7,6,and 9 the triangle is an
Answer by kkasko(45)   (Show Source):
You can put this solution on YOUR website!
If the side of a triangle are 7,6,and 9 the triangle is an scalene triangle since no sides are equal.