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

Find the missing side lengths. Leave your answers as radicals in simplest form-example-1
User Gongshw
by
8.4k points

1 Answer

6 votes

Answer:


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)

User Ho
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