ISEE Upper Level Math : How to find the length of the side of a right triangle

Study concepts, example questions & explanations for ISEE Upper Level Math

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Example Questions

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

A right triangle has a hypotenuse of 10 and a side of 6. What is the missing side?

Possible Answers:

Correct answer:

Explanation:

To find the missing side, use the Pythagorean Theorem . Plug in (remember c is always the hypotenuse!) so that . Simplify and you get Subtract 36 from both sides so that you get Take the square root of both sides. B is 8.

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

Right_triangle

Refer to the above diagram. Which of the following quadratic equations would yield the value of  as a solution?

Possible Answers:

Correct answer:

Explanation:

By the Pythagorean Theorem,

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

Right_triangle

Note: Figure NOT drawn to scale.

Refer to the above diagram. Which of the following quadratic equations would yield the value of  as a solution?

Possible Answers:

Correct answer:

Explanation:

By the Pythagorean Theorem,

Example Question #3 : How To Find The Length Of The Side Of A Right Triangle

Right_triangle

Note: Figure NOT drawn to scale.

Refer to the above diagram.

Find the length of .

Possible Answers:

Correct answer:

Explanation:

First, find .

Since  is an altitude of right  to its hypotenuse, 

 by the Angle-Angle Postulate, so 

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

Right_triangle

Note: Figure NOT drawn to scale.

Refer to the above diagram.

Find the length of .

Possible Answers:

Correct answer:

Explanation:

First, find .

Since  is an altitude of  from its right angle to its hypotenuse, 

 by the Angle-Angle Postulate, so 

Example Question #5 : How To Find The Length Of The Side Of A Right Triangle

Right_triangle

Note: Figure NOT drawn to scale.

Refer to the above diagram. Evaluate .

Possible Answers:

Correct answer:

Explanation:

By the Pythagorean Theorem,

 

Example Question #8 : Triangles

A right triangle  with hypotenuse  is inscribed in , a circle with radius 26. If , evaluate the length of .

Possible Answers:

Insufficient information is given to answer the question.

Correct answer:

Explanation:

The arcs intercepted by a right angle are both semicircles, so hypotenuse  shares its endpoints with two semicircles. This makes  a diameter of the circle, and .

By the Pythagorean Theorem,

 

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