Question

Pls help Applying the 30-60-90 special right triangle rules, find the value of x and y

Answer 1

x = 10, y = 5

Explanation:

The sine of 60 is given by the division of the opposite side of 60º by the hypothenuse.

We have that:

sine of 60 is sqrt(3)/2

The oopposite side is 5sqrt(3)

The hypothenuse is x.

So

`(√(3))/(2)=(5√(3))/(x)`

Then we apply cross multiplication.

`√(3)x=2\ast5√(3)`
`x=(10√(3))/(√(3))=10`

The cosine of 60 is the adjacent side divided by the hypothenuse.

The cosine of 60 is 1/2.

The adjacent side is y.

The hypothenuse is x = 10. So

`(1)/(2)=(y)/(10)`

Applying cross multiplication

2y = 10

y = 5