Tutors Answer Your Questions about Pythagorean-theorem (FREE)
Question 751376: graph h(x) = x^2 - 2
Answer by jim_thompson5910(28593)  (Show Source):
Question 751353: if the length of one leg of a right triangle is 4 and the length of the hypotenuse is 12, what is the length of the other leg?
Answer by JoeTaxpayer(112)  (Show Source):
Question 750525: In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 70 millimeters and b = 24 millimeters, what is the perimeter? If necessary, round to the nearest tenth.
Answer by Cromlix(323)  (Show Source):
You can put this solution on YOUR website!Pythagoras.
a^2 + b^2 = c^2
70^2 + 24^2 = c^2
c^2 = 5476
c = 74 mm
Therefore perimeter
= 70 + 24 + 74 = 168 mm
Hope this helps
:-)
Question 750166: Please could you help me, I've tried and I can't seem to get to anywhere that allows me to work out the x, thank you!
The sides of a right angled triangle are x, (x+2) and (2x-2). The hypotenuse is length (2x-2). Find the actual dimensions of the triangle in cm.
Answer by Alan3354(30993)  (Show Source):
You can put this solution on YOUR website!The sides of a right angled triangle are x, (x+2) and (2x-2). The hypotenuse is length (2x-2). Find the actual dimensions of the triangle in cm.
-------------
Can you do the rest?
-------------
PS "right angled triangle"- call it a right triangle
Question 750174: Hello, I was hoping you could help me, I have tried and tried but I can't work out how to isolate the x to find its value, please help, and thank you in advance!
The sides of a right angled trienagle are x, (x+2) and (2x-2). The hypotenuse is the length (2x-2). Find the actual dimensions of the triangle in cm.
Thank you!
Answer by JoeTaxpayer(112) (Show Source):
You can put this solution on YOUR website!x^2 + (x+2)^2 = (2x-2)^2 is the set up for this equation.
x^2+x^2+4x+4= 4x^2-8x+4 expanded both sides
2x^2+4x+4=4x^2-8x+4
-2x^2+12x=0
2x^2-12x=0
x^2-6x=0
x=0 or x=6
6, 8, 10 are the sides
Question 749806: For a right triangle that has legs a and b and hypotenuse c, find the length of the side not given here.
a = 5 cm
b = 12 cm
Answer by Alan3354(30993) (Show Source):
You can put this solution on YOUR website!For a right triangle that has legs a and b and hypotenuse c, find the length of the side not given here.
a = 5 cm
b = 12 cm
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Question 748707: Equation; S squared = 4 squared + S squared
S squared =___________________
S=___________________
Answer by stanbon(57328) (Show Source):
Question 747214: Consider the three points A = (7, -3), B = (9, 1), and C = (11, 0). Find the
length of each side of the triangle ABC.
Answer by Alan3354(30993) (Show Source):
You can put this solution on YOUR website!Consider the three points A = (7, -3), B = (9, 1), and C = (11, 0). Find the
length of each side of the triangle ABC.
----------------
AB =~ 4.472
--------------
Do the other 2 sides the same way.
Question 746050: Two boats leave the same dock at the same time. One travels north at 6 mph and the other travels east at 8 mph. How far apart will the boats be after 4 hours?
Answer by Alan3354(30993) (Show Source):
You can put this solution on YOUR website!Two boats leave the same dock at the same time. One travels north at 6 mph and the other travels east at 8 mph. How far apart will the boats be after 4 hours?
----------------
It's a right triangle.
Use d = r*t to find the 2 sides, then use Pythagoras to find the hypotenuse.
=================
Question 745697: if the lenghs of the legs of a right triangle are 5 and 12 what is the lengh of the hypotenuse
Answer by Alan3354(30993) (Show Source):
Question 744843: For a right triangle that has legs a and b and hypotenuse c, find the length of the side not given here. a = 5 cm b=12cm
Answer by Cromlix(323) (Show Source):
You can put this solution on YOUR website!This is a Pythagorean question.
The square on the hypotenuse is equal
to the the sum of the squares on the other two sides.
Therefore c^2 = a^2 + b^2
c^2 = 5^2 + 12^2
c^2 = 25 + 144
c^2 = 169
c = the square root of 169
c = 13 cm
Question 717917: a telephone pole breaks and falls as shown. to the nearest foot, what was the original height of the pole? 12ft and 5ft are the sides shown.
Answer by tommyt3rd(528)  (Show Source):
You can put this solution on YOUR website!Assuming that a=5, b=12
then this triangle is clearly in the
family of right triangles. And since the broken part has to be the hypotenuse, the original length had to be the shortest side and hypotenuse:
l=18ft
Question 739103: the hypotenuse of a right triangle is 24 ft long. the length of one leg is 6 feet more than the other. find the length of the legs.
Answer by tommyt3rd(528) (Show Source):
You can put this solution on YOUR website!c=24
Clearly the side we know the least about is the shortest so...
a=x
the length of one leg is 6 feet more than the other means...
b=x+6
So our equation is:
so here we go...
divide by 2...
but this quadratic cannot be factored - so we use the quadratic formula
From which the negative solution can be discarded (why?)
therefore...
and so...
{{a=3sqrt(31)-3}}}
{{b=3sqrt(31)+3}}}
Question 740931: Find the value of x
Right triangle with the sides x, 2x+4, 2x+6
Answer by tommyt3rd(528) (Show Source):
Question 743311: Give an exact answer and, where appropriate, an approximation to three decimal places.
A right triangle's hypotenuse is 8m and one leg is 4 m. Find the length of the other leg.
Answer by stanbon(57328) (Show Source):
You can put this solution on YOUR website!Give an exact answer and, where appropriate, an approximation to three decimal places.
A right triangle's hypotenuse is 8m and one leg is 4 m. Find the length of the other leg.
----
hypo^2 = leg^2 + leg^2
------------
(8m)^2 = [4sqrt(3)m]^2 + leg^2
--------
64m^2 = 16*3*m^2 + leg^2
-------
16m^2 = leg^2
leg = 4m
==================
Cheers,
Stan H.
Question 742447: a rectangular corner lot has sidewalks on two adjacent sides for a total length of 89 feet. if the diagonal path across the lot is 64 feet what is the length of the two sides of the walk? Round answer to two decimal places.
Answer by lwsshak3(6494) (Show Source):
You can put this solution on YOUR website!a rectangular corner lot has sidewalks on two adjacent sides for a total length of 89 feet. if the diagonal path across the lot is 64 feet what is the length of the two sides of the walk? Round answer to two decimal places.
***
Adjacent sides represent two legs of a right triangle with hypotenuse=64 feet
let x=length of one of the sides
89-x=length of other side
x^2+(89-x)^2=64^2
x^2+89^2-178x+x^2=4096
2x^2+7921-178x=4096
2x^2-178x+3825=0
solve for x using quadratic formula:
a=2, b=-178, c=3825
x=36.27
or
x=52.73
length of the two sides of the walk: 36.27 ft and 52.73 ft
Question 742336: A rectangular corner lot has sidewalks on two adjacent sides for a total length of 89 feet. If the diagonal path across the lot is 64 feet, what is the length of the two sides of the walk? Round your answer to two decimal places.
Answer by KMST(1868)  (Show Source):
You can put this solution on YOUR website!Not knowing the width of the sidewalk, we have to assume that the 89 feet of sidewalk were measured along edge of the sidewalk that is also the edge of the lot.
 = length of one edge of the lot, in feet
 = length of the other edge of the lot, in feet
The total length of those two edges that are also the edge of the sidewalk is
 <--> 
the diagonal path across the lot divides the lot into two congruent right triangles. That diagonal path is the hypotenuse of those triangles. The edges of the lot are the legs of those right triangles.
Applying Pythagoras, we get
 --> 
Substituting we get
 -->  --> 
We solve that quadratic equation using the quadratic formula:
That gives us two solutions:
 (rounded) and 
Either value could be , but then the other one would be ,
So the lot measures  by  .
Question 742165: if b:11 in.; and c: 20 in. whats a?
Answer by Alan3354(30993) (Show Source):
Question 739268:
Find the distance between the points with coordinates (-26, 0) and (95, 0)
Answer by checkley79(3050) (Show Source):
Question 738322: Want to make a kite using two rods with fixed length : one of 60cm and one of 40cm.Want to ensure the angle at top corner ( angle ABC ) is a right angle.How far down the rod must you affix the the shorter rod(BE)?
2) What is the smallest available size of material that would be large enough to cut kite shape in 1 whole piece?( Sizes available are squares : 20,40,60,70cm?
3) You want to cut the kite shape out of the square with the top corner(B) aligning with the corner of the square.How far along the side of the square from that corner will you need to cut(to 2 significant figures)?
4)What angle do you need to cut into material?
Please could you help me?
Much Appreciated!!
X
Answer by KMST(1868) (Show Source):
You can put this solution on YOUR website! AE=EC because the kite is symmetrical.
1) For angle ABC to measure  , ABE and EBC must measure  .
That means that in the right triangles ABE and EBC, angles EAB and BCE must measure 
In each of those triangles, both acute angles have the same measure, and that means that those triangles are isosceles, with
The shorter rod should be affixed 20cm from the end of the long rod.
2) The surface area of the kite can be calculated as 1200 square centimeters:
A square with 20cm sides is obviously too small.
A square with 40cm sides will have a surface area of
 , which would provide enough material for the kite.
Can we cut the material in one piece from a 40cm by 40cm square?
Let's see. The 60cm length is hard to accommodate.
The longest straight line segment in a square is the diagonal.
The diagonal splits the square into two isosceles right triangles.
The diagonal is the hypotenuse of those triangles.
In a 40cm by 40cm square, the diagonal's length (in cm) is
That is too short to fit the 60cm length of the kite.
We will need to use the square piece of material measuring
 to a side.
The diagonal of such a square measures
 , long enough to fit the 60cm length of the kite.
3) If we place B at a corner of the square, sides AB and BC are along the sides of the square. We start cutting along lines AD and CD from points at a distance  from the corner of the square.
We can apply the Pythagorean theorem and write
 and since  ,
 --> 
That is about  when rounded to 2 significant figures.
It would be 28.28cm when rounded to 2 decimal places.
4) If we prolong side BC (drawing the side of the square) up to a point P, we can look at the supplementary angles BCD and DCP. Those are the angles made between the edge ot the square of material and the cut to make kite edge CD.
 The measure of angle BCD is the sum of the measures of angles BCE and ECD. We know that angle BCE measures  .
We need to find the measure of angle ECD.
We apply trigonometric ratios to right triangle CDE.
 and we know that  , so
 so ECD measures  (rounding)
and the measure of BCD (rounded) is 
That is the angle of the kite at A an B that we cut from the square of material.
I assume that is the angle meant in the question.
Otherwise, in the material left over we are leaving angle DCP, measuring  . That is the other angle between the cut and the edge of the material.
Question 736858: Triangle PSR is an isosceles triangle with PS=RS. QS
Is perpendicular to PR what is the lenth of QS?
Answer by fcabanski(874) (Show Source):
Question 736462: Evaluate sin^3 7pi divided by 4
THANK YOU!!! you guys are AWESOME!
Answer by josmiceli(9672)  (Show Source):
Question 736279: a walkway forns the diagonal od a square playground. The walkway is 24m long. To the nearest tenth of a meter, how long is a side of the playground?
I did:
x ^2 + x^2 = 24^2
x^4 = 576
x= 4.89 m
but then x^2+x^2 does not equal 24^2
plus the book says the answer is 17 m
Answer by josgarithmetic(1508) (Show Source):
Question 734306: The length of one side of a square is 13 feet. What is the length, to the nearest foot, of a diagonal of the square
Answer by nerdybill(6958)  (Show Source):
You can put this solution on YOUR website!The length of one side of a square is 13 feet. What is the length, to the nearest foot, of a diagonal of the square
.
Apply Pythagorean theorem:
Let d = diagonal
then
d^2 = 13^2 + 13^2
d^2 = 169 + 169
d^2 = 338
d = 18.38
rounded to nearest foot
d = 18 feet
Question 732293: For a right triangle that has legs a, and b, and hypotenuse c, find the length of the side that is not given here.
A=1
C=radical 3
What is B?
Answer by Alan3354(30993) (Show Source):
You can put this solution on YOUR website!For a right triangle that has legs a, and b, and hypotenuse c, find the length of the side that is not given here.
A=1
C=radical 3
What is B?
=================
PS lower case is used for sides, CAPS for the angles.
Question 731551: The difference between bases on a square baseball field is 90 feet. To the nearest tenth, what is the straight-line distance, in feet, from first base to third base?
Answer by checkley79(3050) (Show Source):
Question 730932: A student travel north for 7km and then west for 5 km.how far is the student from the starting point?
Answer by stanbon(57328) (Show Source):
You can put this solution on YOUR website!A student travel north for 7km and then west for 5 km.how far is the student from the starting point?
-----
Assume the student starts at (0,0)
7 km north moves him to (0,7)
5 km west moves him to (-5,7)
----
distance from (0,0) to (-5,7) = ?
-----
d = sqrt[5^2+7^2] = sqrt[25+49] = sqrt[74] = 8.6 km
====================
Cheers,
Stan H.
Question 729273:
1.what is the length of the diagomnal of a rectangle whose length is 16 and whose width is 12?
2.If the legs of a right triangle measure 3 and 4 units,what is the measure of the hypotenuse?
3.The hypotenuse of a right triangle measures 13 and one leg measures 12. what is the measure of the other leg?
Answer by checkley79(3050) (Show Source):
You can put this solution on YOUR website!#1 12^2+16^2=C^2
144+256=C^2
400=C^2
C=SQRT400
C=20 ANS.
#######################
#2
A^2+B^2=C^2
3^2+4^2=C^2
9+16=C^2
25=C^2
C=SQRT25
C=5 ANS.
#####################
YOU SHOULD BE ABLE TO SOLVE THE NEXT ONE.
Question 729281: a soccer field is a rectangle 90 meter wide AND 120 METER LONG. THE COACH ASKS PLAYERS TO RUN FROM ONE CORNER TO THE CORNER DIAGONALLY ACROSS THE FIELD. HOW FAR DO THE PLAYER RUN
Answer by checkley79(3050) (Show Source):
You can put this solution on YOUR website!WHAT YOU HAVE IS A RIGHT TRIANGLE WITH SIDES 90 & 120 METERS.
A^2+B^2=C^2
90^2+120^2=C^2
8,100+14,400=C^2
22,500=C^2
C=SQRT22,500
C=150 METERS IS THE ANSWER FOR THE DIAGONAL DISTANCE.
Question 726738: side a (0,0) to (3,0)
side b (3,0) to (3,4)
find the length of c:
Answer by rfer(12657) (Show Source):
Question 726436: Hello,
Thanks in advance for helping me out with this math problem. I am glad there is someone out there who enjoys helping students on their assignments.
The problem is as followed-
Each year in an ancient land, a large river overflowed its banks, often destroying boundary markers. The royal surveyors used a rope with knots at 12 equal intervals to help reconstruct boundaries. Explain how a surveyor could use this rope to form a right angle. (Hint: Use the Pythagorean triple 3,4, and 5)
Thank you once again....
I understand you would want to know what I think of this problem so far. I think one of the lengths of one ray of the angle is 3 and the other is 4. If it were a triangle the hypotenuse would be 5. However, once I read my answer it doesn't make sense... I know 3 times 4 equals 12? I don't know... Please help. Thank you so much
Answer by mananth(12270)  (Show Source):
Question 725726: a 13 feet ladder is placed 5 feet away from a wall. the distance from the ground straight upto the top of the wall is 13 feet. how far up the wall will the ladder reach?
Answer by checkley79(3050) (Show Source):
You can put this solution on YOUR website!You have a right triangle.
a^2+b^2=c^2
5^2+b^2=13^2
25+b^2=169
b^2=169-25
b^2=144
b=sqrt144
b=12 ft. ans.
Proof:
5^2+12^2=13^2
25+144=169
169=169
Question 725508: Jill's front door is 42 inches wide and 84 just talk soon. She purchased a circular table that is 96 inches in diameter. Will the table fit through the door?
Answer by rajagopalan(158)  (Show Source):
You can put this solution on YOUR website!Jill's front door is 42 inches wide
height = 84
Diagonal=square root of ((42*42)+(84*84))=sq root 8820=93.91
She purchased a circular table that is 96 inches in diameter.
as the table is more in dia than the diagonal,
it will not fit through the door.
Answer : No
Question 725412: 4^2+6^2
Answer by General_Lee87(54)  (Show Source):
You can put this solution on YOUR website!4^2+6^2
4^2=16
First, take 4 to the second power.
6^2=36
Next, take 6 to the second power.
16+36=52
Last, add the two together to get 52.
I hope this helped. Good luck and God Bless.
Question 723405: I need help wih my homework, it says " Determine whether each triangle with sides of given lengths is a right triangle. "
The 1st problem is......
1. 6cm, 8cm, 10cm
How do I figure out whether it's right triangle or not ?
Answer by mananth(12270) (Show Source):
You can put this solution on YOUR website!If it is a right triangle then Pythagoras theorem will hold good.
6, 8 & 10 are the sides.
the largest side is always the hypotenuse
6^2 +8^2
36+64 = 100
10^2= 100
so 6^2+8^2=10^2
therefore it is a right triangle.
Question 723198: 3+4
Answer by unlockmath(1599)  (Show Source):
Question 722165: Given information:
If x represents an even integer, then x+2 represents the next consecutive even integer.
The lengths of the sides of a right triangle are consecutive even integers. Find these lengths. (Hint: Use the Pythagorean theorem.)
Answer by solver91311(16877)  (Show Source):
You can put this solution on YOUR website!
Not enough information to solve this for a specific answer. As stated, any pair of consecutive even numbers satisfies the given conditions. Even if the measure of the hypotenuse were restricted to the rational numbers, there are still infinite solutions to this problem.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
Question 720915: find the area 5 cm , 5 cm , 11 cm , square root 61
Answer by Alan3354(30993) (Show Source):
Question 720097: a right triangle with sides other than hypotenuse is 4cm and 6cm .what is the measure of the hypotenuse.
Answer by god2012(108)  (Show Source):
Question 719640: a right triangle has one leg of 29 length and one leg of 12 length, what is the angle measure of the angle farthest from the right angle?
Answer by Alan3354(30993) (Show Source):
You can put this solution on YOUR website!a right triangle has one leg of 29 length and one leg of 12 length, what is the angle measure of the angle farthest from the right angle?
----------------
The right angle is C, the others are A & B
----
A = atan(12/29) =~ 22.479 degs
B = 90 - A =~ 67.52 degs
Question 718432: a cuboid has dimensions of 10cm, 15cm, and 22,cm and one vertex is at its origin.
Find the length of the diagonal of the cuboid
Answer by stanbon(57328) (Show Source):
You can put this solution on YOUR website!a cuboid has dimensions of 10cm, 15cm, and 22,cm and one vertex is at its origin.
Find the length of the diagonal of the cuboid
-----
base diagonal = sqrt(10^2+15^2) = sqrt(325)
------
cuboid diagonal = sqrt[(sqrt(325))^2 + 22^2]
----
= sqrt[325 + 484]
----
= sqrt[809]
----
= 28.44 cm
================
Cheers,
Stan H.
==================
Question 718333: If a triangle has side lengths of 7 inches, 24 inches, and 25 inches, is it a right triangle? Why is it a right triangle and what is the step by step formula i must use?
Answer by josmiceli(9672) (Show Source):
You can put this solution on YOUR website!All that it needs to be proven a right triangle is
that the Pythagorean-theorem must be true
The square of the longest side must be equal to
the sum of the squares of the other 2 sides.
Yes, it is a right triangle
Question 717423: Two Telephone Poles 22 feet and 29 feet are 70 feet apart, how long is the wire from the top of one pole to the top of the second pole. Wouldnt you account for the fact that one pole is 7 feet taller than the other and use that as leg A and then we know the base is 70 so that would be leg B, then solve for C at 70.35? is that correct?
Answer by KMST(1868) (Show Source):
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