Question

Find the exact side values?

Answer 1

`a = (5 √(2) )/(2)`

`c = (3 √(3) )/(2)`

Explanation:

The first triangle is an isoceles right triangle, so the length of the hypotenuse is √2 times the length of each leg. So we have:

`a √(2) = 5`

`a = (5)/( √(2) ) = (5 √(2) )/(2)`

The second right triangle is a 30°-60°-90° triangle, so the length of the shorter leg is one-half the length of the hypotenuse, and the length of the longer leg is √3 times the length of the shorter leg. Here, the length of the shorter leg is 3/2, or 1.5, and so we have:

`{( (3)/(2)) }^(2) + {c}^(2) = {3}^(2)`

`{c}^(2) = (27)/(4)`

`c = (3 √(3) )/(2)`