Question

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

Answer 1

u = 2√3;

v = 2

Explanation:

Use trigonometry:

`\cos(60°) = (v)/(4)`

Cross-multiply to find v:

`v = 4 * \cos(60°) = 4 * 0.5 = 2`

Use the Pythagorean theorem to find u:

`{u}^(2) = {4}^(2) - {v}^(2)`

`{u}^(2) = {4}^(2) - {2}^(2) = 16 - 4 = 12`

`u > 0`

`u = √(12) = √(4 * 3) = 2 √(3)`