High School Math : How to find the length of the side of a right triangle
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Example Question #1 : How To Find The Length Of The Side Of A Right Triangle
Solve for 
We will use the Pythagorean Theorem to solve for the missing side length.
Example Question #1 : How To Find The Length Of The Side Of A Right Triangle
A square boxing ring has a perimeter of 
Since the perimeter of the ring is 
The distance between the two boxers in opposing corners is a straight line from any one corner to the other. That straight line forms the hypotenuse of a right triangle whose other two sides are each 
Solving for the length of the hypotenuse of this right triangle with the pythagorean theorem 
Example Question #1 : How To Find The Length Of The Side Of A Right Triangle
Given a right triangle with a leg length of 6 and a hypotenuse length of 10, find the length of the other leg, x.
16
8
4
64
8
Using Pythagorean Theorem, we can solve for the length of leg x:
x2 + 62 = 102
Now we solve for x:
x2 + 36 = 100
x2 = 100 – 36
x2 = 64
x = 8
Also note that this is proportionally a 3/4/5 right triangle, which is very common. Always look out for a side-to-hypoteneuse ratio of 3/5 or 4/5, or a side-to-side ratio of 3/4, in any right triangle, so that you may solve such triangles rapidly.
Example Question #1 : How To Find The Length Of The Side Of A Right Triangle
In a right triangle a hypotenuse has a length of 8 and leg has a length of 7. What is the length of the third side to the nearest tenth?
Using the pythagorean theorem, 82=72+x2. Solving for x yields the square root of 15, which is 3.9
Example Question #1 : How To Find The Length Of The Side Of A Right Triangle
Given a right triangle with a leg length of 2 and a hypotenuse length of √8, find the length of the other leg, x.
2
10
√8
4
6
2
Using Pythagorean Theorem, we can solve for the length of leg x:
x2 + 22 = (√8)2 = 8
Now we solve for x:
x2 + 4 = 8
x2 = 8 – 4
x2 = 4
x = 2
Example Question #1 : How To Find The Length Of The Side Of A Right Triangle
The legs of a right triangle are 
Use the Pythagorean Theorem. The sum of both legs squared equals the hypotenuse squared.
Example Question #1 : How To Find The Length Of The Side Of A Right Triangle
Solve for 
(Figure not drawn to scale).
Use the Pythagorean theorem: 
We know the length of one side and the hypotenuse.
Now we can solve for the missing side.
Example Question #2 : How To Find The Length Of The Side Of A Right Triangle
A right triangle has one side equal to 5 and its hypotenuse equal to 14. Its third side is equal to:
9
12
14.87
13.07
171
13.07
The Pythagorean Theorem gives us a2 + b2 = c2 for a right triangle, where c is the hypotenuse and a and b are the smaller sides. Here a is equal to 5 and c is equal to 14, so b2 = 142 – 52 = 171. Therefore b is equal to the square root of 171 or approximately 13.07.
Example Question #1 : How To Find The Length Of The Side Of A Right Triangle
Which of the following could NOT be the lengths of the sides of a right triangle?
5, 7, 10
12, 16, 20
5, 12, 13
14, 48, 50
8, 15, 17
5, 7, 10
We use the Pythagorean Theorem and we calculate that 25 + 49 is not equal to 100.
All of the other answer choices observe the theorem a2 + b2 = c2
Example Question #1 : How To Find The Length Of The Side Of A Right Triangle
Which set of sides could make a right triangle?
4, 6, 9
6, 7, 8
9, 12, 15
10, 12, 16
9, 12, 15
By virtue of the Pythagorean Theorem, in a right triangle the sum of the squares of the smaller two sides equals the square of the largest side. Only 9, 12, and 15 fit this rule.
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