Question

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

Answer 1

x = 3√3;

y = 3

Explanation:

Use trigonometry:

`\sin(30°) = (y)/(6)`

Cross-multiply to find y:

`y = 6 * \sin(30°) = 6 * 0.5 = 3`

Use the Pythagorean theorem to find x:

`{x}^(2) = {6}^(2) - {y}^(2)`

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

`x > 0`

`x = √(27) = √(9 * 3) = 3 √(3)`