Question

Find the value of each variable.
x = and y =

Answer 1

x = 16

y = 27.7

Explanation:

solving for x: use sine

sine =
`(opposite)/(hypotenuse)`

⇒ sine 30 =
`(x)/(32)`

sine of 30 is 0.50

⇒ 0.50 =
`(x)/(32)`

multiply 32 on both sides:

⇒ 0.50 x 32 =
`(x)/(32)` x 32

solve:

⇒ 16 = x

solving for y: use cosine

cosine =
`(adajcent)/(hypotenuse)`

⇒ cosine 30 =
`(y)/(32)`

cosine of 30 is 0.866

⇒ 0.866 =
`(y)/(32)`

multiply 32 on both sides

⇒ 0.866 x 32 =
`(y)/(32)` x 32

solve:

⇒ 27.7 = y

Answer 2

x = 16

y = 16√3

Explanation:

sin(30 degrees) = 1/2

x = 32/2 = 16

cos(30 degrees) = √3/2

y = 16√3