Question

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

Answer 1

`u = (2 √(6) )/(3)`

`v = ( √(6) )/(3)`

Explanation:

Use trigonometry:

`\tan(60°) = ( √(2) )/(v)`

Use the property of proportion to find v:

`v = ( √(2) )/( \tan(60°) ) = ( √(2) )/( √(3) ) = ( √(2) * √(3) )/( √(3) * √(3) ) = ( √(6) )/(3)`

Use the Pythagorean theorem to find u:

`{u}^(2) = {v}^(2) + ( { √(2) )}^(2)`

`{u}^(2) = ( { ( √(6) )/(3)) }^(2) + ( { √(2) )}^(2) = (6)/(9) + (2)/(1) = (6)/(9) + (2 * 9)/(9) = (6)/(9) + (18)/(9) = (24)/(9) = (8)/(3)`

`u > 0`

`u = \sqrt{ (8)/(3) } = (2 √(6) )/(3)`