Question

Find the value of each variable

Answer 1

x = 10
`√(2)` , y = 10
`√(6)`

Explanation:

using the sine and cosine ratios in the right triangle and the exact values

cos60° =
`(1)/(2)` , sin60° =
`(√(3) )/(2)` , then

cos60° =
`(adjacent)/(hypotenuse)` =
`(x)/(20√(2) )` =
`(1)/(2)` ( cross- multiply )

2x = 20
`√(2)` ( divide both sides by 2 )

x = 10
`√(2)`

and

sin60° =
`(opposite)/(hypotenuse)` =
`(y)/(20√(2) )` =
`(√(3) )/(2)` ( cross- multiply )

2y = 20
`√(2)` ×
`√(3)` = 20
`√(6)` ( divide both sides by 2 )

y = 10
`√(6)`