Question

Find the missing side lengths. Leaves your answers as radical in simplest form

Answer 1

v = 2√2

u = 4

Explanation:

Use trigonometry:

`\tan(45°) = (v)/(2 √(2) )`

Cross-multiply to find v:

`v = 2 √(2) * \tan(45°) = 2 √(2) * 1 = 2 √(2)`

Use the Pythagorean theorem to find u:

`{u}^(2) = {v}^(2) + ( {2 √(2) )}^(2)`

`{u}^(2) = ( {2 √(2)) }^(2) + ({2 √(2)) }^(2) = 4 * 2 + 4 * 2 = 8 + 8 = 16`

`u > 0`

`u = √(16) = 4`