# ACT Math : How to find the length of the side of a right triangle

## Example Questions

### Example Question #1 : Right Triangles

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

64

4

8

Explanation:

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 #4 : 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?

3.6
1.0
3.9
2.4
Explanation:

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.

6

4

2

10

√8

2

Explanation:

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  and . Rounded to the nearest whole number, what is the length of the hypotenuse?

Explanation:

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

Points , , and  are collinear (they lie along the same line). , ,

Find the length of segment .

Explanation:

The length of segment is

Note that triangles  and  are both special, 30-60-90 right triangles. Looking specifically at triangle , because we know that segment has a length of 4, we can determine that the length of segment is 2 using what we know about special right triangles. Then, looking at triangle  now, we can use the same rules to determine that segment has a length of

which simplifies to .

### Example Question #82 : Right Triangles

A handicap ramp is  long, and a person traveling the length of the ramp goes up  vertically. What horizontal distance does the ramp cover?