Question

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

Answer 1

x = 6;

y = 3√3

Explanation:

Use trigonometry:

`\ \cos(60°) = (3)/(x)`

Use the property of proportion to find x:

`x = (3)/( \cos(60°) ) = (3)/(0.5) = 6`

Use the Pythagorean theorem to find y:

`{y}^(2) = {x}^(2) - {3}^(2)`

`{y}^(2) = {6}^(2) - {3}^(2) = 36 - 9 = 27`

`y > 0`

`y = √(27) = √(9 * 3) = 3 √(3)`