Question

How do you solve this?

Answer 1

Triginometry. Which side do you want to solve for?

Answer 2

You know all the angles in the triangle 30°, 60°, and 90°. To find the missing sides we will use:

`Sin(opposite)/(hypotenuse) Cos(adjacent)/(hypotenuse) Tan(opposite)/(adjacent)` or
`S(O)/(H) C(A)/(H) T(O)/(A)`

sin 60° =
`(O)/(H)`

sin 60° =
`(x)/(8√(3))`

8√3(sin 60°) = x

8√3(
`(√(3) )/(2)`) = x

12 = x

cos 60° =
`(A)/(H)`

cos 60° =
`(y)/(8√(3) )`

8√3(cos 60°) = y

8√3(
`(1)/(2)`) = y

4√3 = y