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

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

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

Tri 6

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

Possible Answers:

Correct answer:

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

Tri 8

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

Possible Answers:

Correct answer:

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

Tri 9

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

Possible Answers:

Correct answer:

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

Tri 11

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

Possible Answers:

Correct answer:

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.

Possible Answers:

False

True

Correct answer:

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.

Possible Answers:

True

False

Correct answer:

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.

Possible Answers:

False

True

Correct answer:

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

Shape area right triangle

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

Possible Answers:

Correct answer:

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?

Possible Answers:

Correct answer:

Explanation:

 and . However, the included angle of  and , is acute, so its measure is less than that of , which is right. This sets up the conditions of the SAS Inequality Theorem (or Hinge Theorem); the side of lesser length is opposite the angle of lesser measure. Consequently, .

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