Question

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

Answer 1

u = 12;

v = 6

Explanation:

Use trigonometry:

`\tan(60°) = (6 √(3) )/(v)`

Use the property of proportion to find v:

`v = (6 √(3) )/( \tan(60°) ) = (6 √(3) )/( √(3) ) = 6`

Use the Pythagorean theorem to find u:

`{u}^(2) = {v}^(2) + ( {6 √(3)) }^(2)`

`{u}^(2) = {6}^(2) + ( {6 √(3)) }^(2) = 36 + 36 * 3 = 36 + 108 = 144`

`u > 0`

`u = √(144) = 12`