Question

Find the missing side lengths leave your answerss as radicals

Answer 1

x = 8, y = 4

Explanation:

To find x use the sine ratio in the right triangle and the exact value

sin60° =
`(√(3) )/(2)` , thus

sin60° =
`(opposite)/(hypotenuse)` =
`(4√(3) )/(x)` =
`(√(3) )/(2)` ( cross- multiply )

x ×
`√(3)` = 8
`√(3)` ( divide both sides by
`√(3)` )

x = 8

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To find y use the tangent ratio in the right triangle and the exact value

tan60° =
`√(3)` , thus

tan60° =
`(opposite)/(adjacent)` =
`(4√(3) )/(y)` =
`√(3)` ( multiply both sides by y )

4
`√(3)` = y ×
`√(3)` ( divide both sides by
`√(3)` )

y = 4