# Basic Geometry : How to find the length of the side of a right triangle

## Example Questions

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### Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

What is the length of the remaining side of the right triangle?

Explanation:

Rearrange the Pythagorean Theorem to find the missing side. The Pythagorean Theorem is:

where  is the hypotenuse and and  are the sides.

### Example Question #2 : How To Find The Length Of The Side Of A Right Triangle

The hypotenuse of a right triangle is 26 in and one leg is 10 in.  What is the sum of the two shortest sides?

Explanation:

We use the Pythagorean Theorem so the problem to solve becomes where = unknown leg length

So and

The sum of the two legs becomes

Explanation:

### Example Question #4 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the unknown side, , of the right triangle below.

Explanation:

We need to use the Pythagorean Theorem, which says that .

Since we need to find the length of 'a', we can just solve for 'a'.

In our case, c = 12 and b = 9.

Thus, .

### Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

Find the missing leg of the right triangle when one of the legs is  and the hypotenuse is .

Explanation:

In order to find the missing side of a right triangle you must use one of two things:

1. Pythagorean Theorem

2. Trigonometry.

Since we only know what the side lengths are we must use the Pythagorean Theorem.

a=4, b=x, and c=5

So the missing side length is 3

### Example Question #6 : How To Find The Length Of The Side Of A Right Triangle

Given that the hypotenuse of a right triangle is  and one side is , find the other side length.

Explanation:

To find the length of the missing side, you can either use the pythagorean theorm or realize this is a case of a special right triangle with sides .

Thus, the other side length is .

### Example Question #6 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

Explanation:

Recall the Pythagorean Theorem for a right triangle:

Since the missing side corresponds to side , rewrite the Pythagorean Theorem and solve for .

Now, plug in values of  and  into a calculator to find the length of side . Round to  decimal places.

### Example Question #7 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

Explanation:

Recall the Pythagorean Theorem for a right triangle:

Since the missing side corresponds to side , rewrite the Pythagorean Theorem and solve for .

Now, plug in values of  and  into a calculator to find the length of side . Round to  decimal places.

### Example Question #2 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

Explanation:

Recall the Pythagorean Theorem for a right triangle:

Since the missing side corresponds to side , rewrite the Pythagorean Theorem and solve for .

Now, plug in values of  and  into a calculator to find the length of side . Round to  decimal places.

### Example Question #9 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side length.

Explanation:

Recall the Pythagorean Theorem for a right triangle:

Since the missing side corresponds to side , rewrite the Pythagorean Theorem and solve for .

Now, plug in values of  and  into a calculator to find the length of side . Round to  decimal places.

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