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

## Example Questions

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### Example Question #21 : How To Find The Length Of The Side Of A Right Triangle

Given the right triangle above, find the length of the missing side.

Explanation:

To find the length of the side x, we must use the Pythagorean Theorem

.

However, this time since we are given the value of the hypotenuse, we will solve for side b rather than c.

So, when we plug the given values into the formula, the equation looks like

which can be simplified to

.

Next, solve for b and we get a final answer of

.

This particular example is a Pythagorean triple, or a right triangle with 3 whole number values, so it is a good one to remember.

### Example Question #22 : How To Find The Length Of The Side Of A Right Triangle

Given the above right triangle, find the length of the missing side.

Explanation:

To find the length of the side x, we must use the Pythagorean Theorem

.

However, this time since we are given the value of the hypotenuse, we will solve for side b rather than c.

So, when we plug the given values into the formula, the equation looks like

which can be simplified to

.

Next, solve for b and we get a final answer of

.

### Example Question #23 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side of the right triangle.

Explanation:

To find the length of the side x, we must use the Pythagorean Theorem

.

However, this time since we are given the value of the hypotenuse, we will solve for side b rather than c.

So, when we plug the given values into the formula, the equation looks like

which can be simplified to

.

Next, solve for b and we get a final answer of

.

### Example Question #21 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side of the right triangle.

Explanation:

To find the length of the side x, we must use the Pythagorean Theorem

.

However, this time since we are given the value of the hypotenuse, we will solve for side b rather than c.

So, when we plug the given values into the formula, the equation looks like

which can be simplified to

.

Next, solve for b and we get a final answer of

.

### Example Question #25 : How To Find The Length Of The Side Of A Right Triangle

The three sides of a triangle have lengths  , and .

True or false: the triangle is a right triangle.

False

True

False

Explanation:

We can rewrite each of these fractional lengths in terms of their least common denominator, which is , as follows:

By the Pythagorean Theorem and its converse, a triangle is right if and only if

,

where  is the length of the longest side and  and  are the lengths of the other two sides.

Therefore, we can set , and test the truth of the statement:

The statement is false, so the Pythagorean relationship does not hold. The triangle is not right.

### Example Question #26 : How To Find The Length Of The Side Of A Right Triangle

The three sides of a triangle have lengths 0.8, 1.2, and 1.5.

True or false: the triangle is a right triangle.

True

False

False

Explanation:

By the Pythagorean Theorem and its converse, a triangle is right if and only if

,

where  is the length of the longest side and  and  are the lengths of the other two sides.

Therefore, set  and test the statement for truth or falsity:

The statement is false, so the Pythagorean relationship does not hold. The triangle is not right.

### Example Question #27 : How To Find The Length Of The Side Of A Right Triangle

The three sides of a triangle have lengths , and .

True or false: the triangle is a right triangle.

False

True

True

Explanation:

By the Pythagorean Theorem and its converse, a triangle is right if and only if

,

where  is the length of the longest side and  and  are the lengths of the other two sides.

Therefore, we can set , and test the truth of the statement:

The statement is true, so the Pythagorean relationship holds. The triangle is right.

### Example Question #28 : How To Find The Length Of The Side Of A Right Triangle

In the right triangle shown here,  and . What is the length of the base ?

Explanation:

Given the lengths of two sides of a right triangle, it is always possible to calculate the length of the third side using the Pythagorean Theorem:

Here, the given side lengths are  and . Solving for  yields:

.

Hence, the length of the base  of the given right triangle is  units.

### Example Question #29 : How To Find The Length Of The Side Of A Right Triangle

Given:  and .

is an acute angle;  is a right angle.

Which is a true statement?