Question

Find the missing side lengths. Leave your answers as radicals in simplest form

Answer 1

`x = y = (5 √(2) )/(2)`

Explanation:

Use trigonometry:

`\sin(45°) = (x)/(5)`

Cross-multiply to find x:

`x = 5 * \sin(45°) = 5 * ( √(2) )/(2) = (5 √(2) )/(2)`

Use the Pythagorean theorem to find y:

`{y}^(2) = {5}^(2) - {x}^(2)`

`{y}^(2) = {5}^(2) - ( { (5 √(2) )/(2)) }^(2) = 25 - (25 * 2)/(4) = (25)/(1) - (50)/(4) = (25 * 4)/(4) - (50)/(4) = (100)/(4) - (50)/(4) = (50)/(4) = (25)/(2)`

`y > 0`

`y = \sqrt{ (25)/(2) } = (5 √(2) )/(2)`