# Questions on Geometry: Pythagorean theorem answered by real tutors!

Algebra ->  Pythagorean-theorem -> Questions on Geometry: Pythagorean theorem answered by real tutors!      Log On

Question 993434: Using the Pythagorean Theorem where a and c are known and b is unknown. How do I solve this problem.
Drive A is heading East and Driver B is heading North. After 30 mins Driver A has gone 20 miles and Driver B has gone 21 miles. How far apart are Drivers A and B after 30 mins of traveling?

Found 2 solutions by Cromlix, davidrolf:
Answer by Cromlix(3061)   (Show Source):
You can put this solution on YOUR website!
Hi there,
Consider a right angled triangle.
Driver heading East is the base
Driver heading North is the upright.
Distance apart is the hypotenuse.
A^2 + B^2 = C^2
20^2 + 21^2 = C^2
400 + 441 = C^2
C = √(400 + 441)
C = √(841)
C = 29 miles
Hope this helps :-)

Answer by davidrolf(2)   (Show Source):
You can put this solution on YOUR website!
Hi.
I call distance apart for c
c=sqrt(21^2+20^2)
c=29 miles

Question 993063: Please make sure your answers to the following questions are in Radical Form.
Grace and Chandler met for lunch. At 1 p.m., they parted ways. Maybe forever, considering how they left things. Chandler drove due south at 30 mph and Grace drove due east at 60 mph. Apparently, she was more upset than he was. At 2:30 p.m., how far away are Grace and Chandler?
It says that I have to use the Pythagorean Theorem to write an equation that will help solve my problem. Then I must write in a sentence my answer, and explaining what it means. I understand what that is and how you do it. I just don't understand how to do it all in Radical Form.

Answer by stanbon(69061)   (Show Source):
You can put this solution on YOUR website!
Grace and Chandler met for lunch. At 1 p.m., they parted ways. Maybe forever, considering how they left things. Chandler drove due south at 30 mph and Grace drove due east at 60 mph. Apparently, she was more upset than he was. At 2:30 p.m., how far away are Grace and Chandler?
-----
Chandler distance:: 30*(3/2 hr) = 45 miles
Grace distance:: 60(3/2 hr) = 90 miles
-----
Draw the right triangle with legs of 45 and 90.
Ans: dist = hypotenuse = sqrt[45^2+90^2] = sqrt(10125)
= sqrt[25*81*5] = 5*9sqrt(5) = 45sqrt(5) miles
--------
Cheers,
Stan H.

Question 992781: consider the right triangle where a=3 and b=3 what is the value of c written in simple radical form and rounded to the nearest hundredth

Answer by stanbon(69061)   (Show Source):
You can put this solution on YOUR website!
consider the right triangle where a=3 and b=3 what is the value of c written in simple radical form and rounded to the nearest hundredth
---
c = sqrt[3^2 + 3^2] = sqrt[2*3^2} = 3*sqrt(2)
--------------
cheers,
Stan H.
---------

Question 992744: The sides of a rectangular swimming pool are 50m & 30m. What is the distance in meters of the opposite corners?
Answer by Cromlix(3061)   (Show Source):
You can put this solution on YOUR website!
Hi there,
Consider the pool as a right angled triangle.
So, 30^2 + 50^2 = (distance of opposite corners)^2
=> 900 + 2,500 = (distance of opposite corners)^2
=> 3,400 = (distance of opposite corners)^2
=> (distance of opposite corners) = sqrt 3400
=> distance of opposite corners = 58.31 meters (2 decimal places)
Hope this helps :-)

Question 992722: i was wondering if there was a way that if you had a right triangles hypotenuse, if you can find the lengths of the legs?
Answer by josgarithmetic(13975)   (Show Source):
You can put this solution on YOUR website!
A leg or an angle.

Question 991811: Suppose there is a right triangle with 2 legs of 7 cm and 11 cm long. What is the measurement of the hypotenuse?
Answer by ikleyn(988)   (Show Source):
You can put this solution on YOUR website!
.
What is the measure of the hypotenuse of a right triangle with the legs of 7 cm and 11 cm long?
----------------------------------------------------------------------------

= = cm.

Question 990912: My Question Is The Length Of A Diagonal Of A Rectangle Lawn Is 30cm And The Length Of One Side Is 24cm . Find The Perimeter.
Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
Duplicate.
----
And, that's not a question.

Question 990911: My Question Is The Length Of At Diagonal Of A Rectangle Lawn Is 30cm And The Length Of One Side Is 24cm .Find The Perimeter
Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
The diagonal is the hypotenuse of a right triangle.
---------------------------
c = diagonal = 30 cm

Find the other side.
----------
Then, the perimeter = 2L + 2W where L and W are the sides.
----------------------
That's some "lawn" - about 2 inches on a side. Is this for a doll house?

Question 990594: ABCD is a rhombus of side 15cm. The diagonal AC is of length 20cm. Find the angle between AC and the side CD.
Answer by Boreal(1464)   (Show Source):
You can put this solution on YOUR website!
The diagonals are perpendicular to each other and bisect each other.
Therefore, the two legs of the right triangle are the sides of each diagonal and the side CD is the hypotenuse.
The angle is the adjacent side (10, half of the diagonal) divided by 15, the hypotenuse. That is the cosine, so cos of x=10/15
The arc cos of (10/15) is 48.2 degrees.

Question 990380: If area of a rectangle is 52inches squared and the base is 4 inches what is the height
Answer by macston(4006)   (Show Source):
You can put this solution on YOUR website!
.
A=area; b=base; h=height
.
b*h=A
h=A/b
h=52in^2/4in
h=13in
ANSWER: The height is 13 inches.

Question 990322: A rectangular shaped telivison screen measures 26" across on of the diagonals. What is the measure of the othe diagonal?
Answer by josgarithmetic(13975)   (Show Source):
You can put this solution on YOUR website!
The television screen is a rectangle. Diagonal question already answered.

Question 989757: I am having a hard time solving this problem, im completely drawing a blank.
The equation is: the hypotenuse of a right triangle is 20cm and one leg is 16cm. Find the length of the other leg. And find the area of the triangle.

Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
I am having a hard time solving this problem, im completely drawing a blank.
The equation is: the hypotenuse of a right triangle is 20cm and one leg is 16cm. Find the length of the other leg. And find the area of the triangle.
================
Other leg =

Answer by ikleyn(988)   (Show Source):
You can put this solution on YOUR website!
.
Do you know the Pythagorean theorem?

It says that the other leg is    = = = = 4*3 = 12.

Could you find the area of the triangle then?

Question 989742: A tree from the ground at a height of 5 meters are broken. And the upper extremity touching distance of 12 meters from the ground to the base. Please find the full height of the tree.
Answer by ikleyn(988)   (Show Source):
You can put this solution on YOUR website!
.
It is

= = = 13 meters.

Question 989688: A three-foot kiddy slide must meet the ground very gradually, making an angle of 155 degrees. Find the height and the length of the floor it will cover. Help I've tried this and can't get it
Answer by josgarithmetic(13975)   (Show Source):
You can put this solution on YOUR website!
The only way to understand this is the 155 degree is the ladder turned or rotated keeping one end fixed, sweeping through 155 degrees, also making an angle on the acute part of 25 degrees. The ladder is no longer over the original position where it was, on the ground.

Now, you have a y number foot high side opposite of a 25 degree angle. One angle of this triangle is 90 degrees. The hypotenuse is 3 feet. You want to know y and the other leg.

y, the height
x, the leg on the ground

Question 989471: How to find the area of a rectangle whose length is 12 and whose diagonal is 13?
Answer by MathLover1(11324)   (Show Source):
You can put this solution on YOUR website!

a diagonal divides a rectangle in two right angle triangles; so, use Pythagorean theorem
if the length is and whose diagonal is , than the width will be

so, the length is and the width is
the area will be:

Question 989149: ABC is an equilateral triangle in which BC=2cm. Find the perpendicular distance from A to BC.
Answer by macston(4006)   (Show Source):
You can put this solution on YOUR website!
.
The perpendicular forms a right triangle with hypotenuse AB=2cm,
one leg is 1/2(BC)=1cm.
.
Let c=AB=2cm, b=1/2(BC)=1cm, a=perpendicular distance from A to BC
.

.
ANSWER: The perpendicular distance is .

Question 988271: A 40 foot tower is to be fastened by three guy wires attached to the top of the tower and the ground at positions 20 feet from its base. How much wire is needed? Round to the nearest tenth
Answer by Cromlix(3061)   (Show Source):
You can put this solution on YOUR website!
Hi there,
Consider the mast and wires as a right
angled triangle.
The wire is the hypotenuse
The mast is the opposite side
The mast size^2 + ground length^2
= wire length^2
So, 40^2 + 20^2 = wire length^2
1600 + 400 = wire length^2
wire length^2 = 2000
wire length = √2000
wire length = 44.721
3 wires = 3 x 44.721
3 wires = 134.2ft
Hope this helps :-)

Question 988155: The midpoint of uv is (5 -11). The coordinates of one endpoint are u(3,5). Find the coordinates of endpoint v.
Answer by josgarithmetic(13975)   (Show Source):
You can put this solution on YOUR website!
You want the unknown point (x,y) so that .

Question 987535: The legs of a right isoceles triangle are each √71 feet. How long is the hypotenus of this triangle? Round your answer to the nearest whole number.
Found 2 solutions by jim_thompson5910, josgarithmetic:
Answer by jim_thompson5910(33401)   (Show Source):
You can put this solution on YOUR website!

Plug in the given leg measurements

Square the square roots.

Apply the square root to both sides

Use a calculator

Round to the nearest whole number

The hypotenuse is approximately 12 feet long

Answer by josgarithmetic(13975)   (Show Source):
You can put this solution on YOUR website!
The triangle described must have the right angle between the two equal sides.

h for hypotenuse;

or

Question 987355: Ellen wants to put some edging around her lawn
The lawn is in the shape of a right-angle triangle
The edging is sold in pieces 110cm long and 20cm high
The price of each piece is £5
Calculate how much it will cost Ellen to do the job
The lengths of the lawn is 6m high and 4m long
could you show me the method please

Answer by stanbon(69061)   (Show Source):
You can put this solution on YOUR website!
Ellen wants to put some edging around her lawn
The lawn is in the shape of a right-angle triangle
The edging is sold in pieces 110cm long and 20cm high
The price of each piece is £5
Calculate how much it will cost Ellen to do the job
The lengths of the lawn is 6m high and 4m long
--------
Draw a right triangle with legs of 6m and 4m
Find the hypotenuse::
h = sqrt(6^2+4^2) = sqrt(36+16) = sqrt(52) = sqrt(4*13) = 2sqrt(13)
-----------------
Perimeter of the triangle = 6+4+2sqrt(13) = [10+2sqrt(13)] meters
------
Convert to centimeters:: (10+2sqrt(13)*100 = (1000+200sqrt(13))cm
------------------------
Ans::# of pieces needed:: (1000+200sqrt(13))/110
=====
Cost = $5[1000+200sqrt(13))/110 = (1000+200sqrt(13))/22 =$76.95
-------------
Cheers,
Stan H.

Question 987219: The length of the longer leg of a right triangle is
6m more than twice the length of the shorter leg. The length of the hypotenuse is 9m more than twice the length of the shorter leg. Find the side lengths of the triangle. Thank you

Found 2 solutions by stanbon, solver91311:
Answer by stanbon(69061)   (Show Source):
You can put this solution on YOUR website!
The length of the longer leg of a right triangle is
6m more than twice the length of the shorter leg. The length of the hypotenuse is 9m more than twice the length of the shorter leg. Find the side lengths of the triangle. Thank you
-------
shorter leg: x
longer leg:: 2x+6
hypot:: 2x+9
-----------------------
Equation:
(2x+9)^2 = x^2 + (2x+6)^2
------
4x^2 + 36x + 81 = x^2 + 4x^2 + 24x + 36
-------
x^2 -12x - 45 = 0
------
x = 15
----
Ans:
shorter leg = 15
longer leg = 36
----------
Cheers,
Stan H.
---------------

Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!

The sides are , , and . Plug these expressions into the Pythagorean Theorem and solve for . Then calculate and .

Note that any negative value for would be absurd; exclude any negative root.

John

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

Question 986916: The lengths of two sides of right triangle are given. Find the missing side length. Give the exact answer and an approximation to the nearest hundredth.
B=6mm and C=15mm

Answer by ankor@dixie-net.com(18980)   (Show Source):
You can put this solution on YOUR website!
The lengths of two sides of right triangle are given.
Find the missing side length.
Give the exact answer and an approximation to the nearest hundredth.
B=6mm and C=15mm
:
A^2 + 6^2 = 15^2
A^2 + 36 = 225
A^2 = 225 - 36
A^2 = 189
A = or exact simplified
A = 13.75

Question 986912: A 50 foot tower is to be fastened by five guy wires attached to the top of the tower and to the ground at positions 30 feet from its base. How much wire is needed ? Round to the nearest tenth.
Answer by stanbon(69061)   (Show Source):
You can put this solution on YOUR website!
A 50 foot tower is to be fastened by five guy wires attached to the top of the tower and to the ground at positions 30 feet from its base. How much wire is needed ? Round to the nearest tenth.
-------
Draw a picture of the tower, one of the wires and the 30 ft base.
You have a right triangle.
Solve for the hypotenuse::
h = sqrt(50^2+30^2) = 58.31 ft
----
Ans: Since there are 5 wires you need 5*58.31 = 291.55 ft of wire
----------
Cheers,
Stan H.
----------

Question 986779: One leg Of a right triangle Is 5 inches lInter than the other. If the hypotenuse is 25 inches long, Find the lengths of the legs.(only an algerbraic solution will be accepted)
Answer by Cromlix(3061)   (Show Source):
You can put this solution on YOUR website!
Hi there,
One leg is 5 ins. shorter than
other leg.
Other leg = 'x'
One leg = x - 5
Hypotenuse = 25 ins
x^2 + (x - 5)^2 = 25^2
x^2 + x^2 - 10 + 25 = 625
2x^2 - 10x - 600 = 0
Divide thro' by 2
x^2 - 5x - 300 = 0
Factorise
(x - 20)(x + 15) = 0
x + 15 = 0
x = -15 (no answer as -ve)
x - 20 = 0
x = 20
Other leg = 20 inches
One leg = 15 inches
Hypotenuse = 25 inches.
Hope this helps :-)

Question 986627: Hi my name is Gabi and I'm trying to do this problem A(0,0),B(8,6) it says that I need to use the Pythagorean theorem to find the distance between each pair of point and I don't really know how to use it
Answer by stanbon(69061)   (Show Source):
You can put this solution on YOUR website!
Hi my name is Gabi and I'm trying to do this problem A(0,0),B(8,6) it says that I need to use the Pythagorean theorem to find the distance between each pair of points and I don't really know how to use it.
-----
If you have two points (a,b) and (c,d)
the distance between them is
D = sqrt[(a-c)^2 + (b-d)^2]
------------------------------
D = sqrt[(8-0)^2 + (6-0)]^2
----
D = sqrt[64+36] = sqrt(100) = 10
-----------
Cheers,
Stan H.
------------

Question 986124: The shorter sides of an acute triangle are x cm and 2x cm. The longest side of the triangle is 15 cm.
What is the smallest possible whole-number value of x?

Answer by vleith(2950)   (Show Source):
You can put this solution on YOUR website!
The sum of any two sides of a triangle must be greater than the remaining side.
so

The smallest whole number greater than 5 is 6

Question 985613: How do you round a square rooted number to the nearest tenth
Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!

The same way you round any decimal fraction to the nearest tenth. Look at the digit in the hundredths column. If it is 5 or larger, increase the digit in the tenths column by 1, otherwise leave the digit in the tenths column alone. Only report your answer with one decimal place of accuracy.

Also note that if your square root is the root of a perfect square and the answer is a whole number, you have to add the .0 on the end to make it rounded to the nearest tenth.

For example:

Rounded to the nearest tenth, 1.4

Rounded to the nearest tenth, 9.7 (the hundreths digit is > 5, so plus up the tenths)

But rounded to the nearest tenth, 10.0

John

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

Question 984686: A suitcase measures 24 inches long, 18 inches high, and 12 inches deep. What is the longest stick you could place in the suitcase to the nearest tenth of a foot?
Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!

Use the Pythagorean Theorem to find the diagonal of a rectangle with sides of 24 inches and 18 inches. Then use Pythagoras again to find the diagonal of a rectangle that is 12 inches by the answer to your first computation. Now you have the length of the stick in inches, so long as the stick is not too thick. Do not round the answer yet. Divide by 12. Now round to the nearest 10th.

John

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

Question 984505: a=x
b=x+12
C=60
help would be sooooo appreciated

Answer by vleith(2950)   (Show Source):
You can put this solution on YOUR website!
Right triangle with sides a and b and hypotenuse c
You know that
So plug in the given values

 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=7056 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 36, -48. Here's your graph:

That yields two solutions. But one is negative. A triangle can't have a side with negative length, so use the positive one. Once you know a, then b = 12 more
a=36
b=48

Question 984327: Please help me with this Question.,A chord of lenght 24cm is 13cm from the centre of the circle. Calculate the radius of the circle.And (the distance of a chord of a circle,or radius 5cm,from the centre is 4cm.calculate the lenght of the chord)
Found 2 solutions by solver91311, ikleyn:
Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!

See diagram

John

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

Answer by ikleyn(988)   (Show Source):
You can put this solution on YOUR website!

--------------------------------------------------------------------
1. A chord of length  24 cm  is  13 cm  from the center of the circle.
Calculate the radius of the circle.
--------------------------------------------------------------------

What you are given is in the Figure 1.
 Figure 3.

Find the radius  r  as the hypotenuse of the right-angled triangle with the legs  12 cm  and  13 cm:

= = = = (approximately).

Question 984064: The front wall of the house is in the shape of equilateral triangle. The base of the house is 10m long. How tall is the front of the house

Answer by josgarithmetic(13975)   (Show Source):
You can put this solution on YOUR website!
Base of house, bottom side of equilateral triangle wall?

Tip to middle of base, altitude. Half of base is 5 meters. Two legs of resulting right triangle are 5 and y. 10 is a side of the equilateral and hypotenuse of one of the right triangles.

Find y.

Question 983927: what is the total length of a triangle if one side equals 337 and another equals 9?

Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!

All you can know for sure is that the measure of the third side is in the interval

Note the strictly less than relationship.

John

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

Question 982865: X^2+(x+6)^2=(x+12)^2
I got the answer with trial an error. But i don't understand how to show the work.
(Finding the lengths of all legs of a right triangle)

Found 2 solutions by ankor@dixie-net.com, stanbon:
Answer by ankor@dixie-net.com(18980)   (Show Source):
You can put this solution on YOUR website!
X^2 + (x+6)^2 = (x+12)^2
FOIL (x+6)(x+6) and (x+12)(x+12)
x^2 + x^2 + 12x + 36 = x^2 + 24x + 144
Collect like terms on the left
x^2 + x^2 - x^2 + 12x - 24x + 36 - 144 = 0
x^2 - 12x - 108 = 0
You can use the quadratic formula a=1; b=-12, c=-108; but this will factor to
(x - 18)(x + 6) = 0
It's the positive solution we want here
x = 18 is one side
then
18 + 6 = 24 is the other side
and
18 + 12 = 30 is the hypotenuse

Answer by stanbon(69061)   (Show Source):
You can put this solution on YOUR website!
X^2+(x+6)^2=(x+12)^2
I got the answer with trial an error. But i don't understand how to show the work.
(Finding the lengths of all legs of a right triangle)
=======
X^2+(x+6)^2=(x+12)^2
------
x^2 + x^2 + 12x + 36 = x^2 + 24x + 144
------
x^2 - 12x - 108 = 0
-------
(x-18)(x+6) = 0
-------
Positive solution::
x = 18
--------
Cheers,
Stan H.
--------

Question 982519: leg A is 7' attached to leg C at a right angle. Leg B is attached to leg A and B and is 28' long. What is the length of leg C?
Answer by Fombitz(25151)   (Show Source):

Question 982346: James built a box with dimensions 30cm long, 12cm wide and 20cm high what is the longest paintbrush that can be stored in the box
Show working out please

Answer by josgarithmetic(13975)   (Show Source):
You can put this solution on YOUR website!
Three-Dimensioned Pythagorean Theorem, using the longest diagonal as if it were 3-D hypotenuse.

Question 982341: a rectangular box is completely filled with dice. Each dice has a volume of 1 cubic cm. Suppose the box holds at most 140 dice. What are the possible dimensions of the box?
Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!

There are lots of possibilities:

There are several more, you can work them out for yourself.

John

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

Question 982287: In Angle ABC, C is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth.
a = 3, c = 19

Answer by josgarithmetic(13975)   (Show Source):
You can put this solution on YOUR website!
Draw this triangle. A, over to the right. C to the left, B a little above C.
The right angle is at C. c is opposite C; a is opposite of A, and b is opposite of B.

These you know as given:
a=3,c=19, measure at angle C is 90 degrees.

-------b is now known.

Find at least angle A or B, and the other can be quickly found by angle sum to 180 degree.
Here is the most sensible choice: and then .

-
A, B, C, used here both as variables for each angle as well as for naming the points

Question 982284: . In , is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth. Show your work.

a = 3, c = 19

Answer by solver91311(20879)   (Show Source):
You can put this solution on YOUR website!

Can't help you. You left out part of the problem.

John

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

Question 981787: verify the identity
cot(theta+pi/2)=-tan(theta)

Answer by ikleyn(988)   (Show Source):
You can put this solution on YOUR website!

1.   = .

2.   =     (apply the formula for cosines of the sum of angles,  see the lesson  Addition and subtraction formulas  in this site,  or any textbook on Trigonometry)
= . - . = . - . = .

3.   =     (apply the formula for sines of the sum of angles,  see the same lesson  Addition and subtraction formulas  in this site,  or any textbook on Trigonometry)
= . + . = . + . = .

Hence,   = = = .

Conclusion.  The identity   =   which was proposed you to verify,  is true.