Question

Find the value of each variable for the right triangles. make sure all answers are in reduced radical form. show your work.

Answer 1

Hi there! The answer is 3 multiplied by the square root of 13.

Using the following theorem (Pythagorean Theorem), with a and b representing rectangular sides and c representing the hypotenuse, and the numbers from the picture, we get the following:


`{a}^(2) + {b}^(2) = c {}^(2)`

Fill in the numbers

`{6}^(2) + { 9}^(2) = c {}^(2)`

Work out the powers

`36 + 81 = {c}^(2)`

Add up

`{c}^(2) = 117`

Take the square root of both sides.

`c = √(117) = 3 √(13)`