Question

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

Answer 1

y = 2;

x = 2√2

.

Explanation:

Use trigonometry:

`\tan(45°) = (y)/(2)`

Use the property of proportion to find x (cross-multiply):

`y = 2 * \tan(45°) = 2 * 1 = 2`

Use the Pythagorean theorem to find x:

`{x}^(2) = {y}^(2) + {2}^(2)`

`{x}^(2) = {2}^(2) + {2}^(2) = 4 + 4 = 8`

`x > 0`

`x = √(8) = √(4 * 2) = 2 √(2)`