Question

Find x and y. Please write your answer in simplified radical form.

Answer 1

see explanation

Explanation:

Using the sine and cosine ratios in the right triangle

sin30° =
`(opposite)/(hypotenuse)` =
`(6)/(y)`

Multiply both sides by y

y × sin30° = 6 ( divide both sides by sin30° )

y =
`(6)/(sin30)` =
`(6)/((1)/(2) )` = 12

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cos30° =
`(adjacent)/(hypotenuse)` =
`(x)/(y)`

Multiply both sides by y ( y = 12 )

12 × cos30° = x

x = 12 ×
`(√(3) )/(2)` = 6
`√(3)`