Question

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

Answer 1

x = 5;

`y = (5 √(2) )/(2)`

Explanation:

Use trigonometry:

`y = \tan(45°) = ( (5 √(2) )/(2) )/(y)`

Use the property of proportion to find y:

`y = ( (5 √(2) )/(2) )/( \tan(45°) ) = ( (5 √(2) )/(2) )/(1) = (5 √(2) )/(2)`

Use the Pythagorean theorem to find x:

`{x}^(2) = {y}^(2) + { ((5 √(2) )/(2)) }^(2)`

`{x}^(2) = {( (5 √(2) )/(2)) }^(2) + { ((5 √(2) )/(2)) }^(2) = (25 * 2)/(4) + (25 * 2)/(4) = (50)/(4) + (50)/(4) = (100)/(4) = 25`

`x > 0`

`x = √(25) = 5`