Question

What are the values of x and y?
image attached. Thank you!

Answer 1

C

Explanation:

Using the cosine/ sine ratio in the right triangle and the exact values

cos30° =
`(√(3) )/(2)` and sin30° =
`(1)/(2)` , then

cos30° =
`(adjacent)/(hypotenuse)` =
`(BC)/(AC)` =
`(x)/(18)` =
`(√(3) )/(2)` ( cross- multiply )

2x = 18
`√(3)` ( divide both sides by 2 )

x = 9
`√(3)`

----------------------------------------------------------

sin30° =
`(opposite)/(hypotenuse)` =
`(AB)/(AC)` =
`(y)/(18)` =
`(1)/(2)` ( cross- multiply )

2y = 18 ( divide both sides by 2 )

y = 9

Thus

x = 9
`√(3)` and y = 9 → C

Answer 2

C

Explanation:

We'll have to use trigonometry for this.

First, note that in right triangle ABC, if we look from the perspective of angle A, the opposite side is x, the adjacent side is y, and the hypotenuse is 18.

In order to find x, then, we must use sine, which is opposite/hypotenuse. So:

sin(A) = sin(60) = opposite/hypotenuse = x/18

sin(60) is equal to (√3)/2, so multiplying both sides by 18 gives:

[(√3)/2] * 18 = 9√3

Already, we can tell that the answer is likely C, but let's find y to make sure.

We will use cosine to find y because cos = adjacent/hypotenuse.

cos(A) = cos(60) = adjacent/hypotenuse = y/18

cos(60) = 0.5, so multiplying both sides by 18 gives:

0.5 * 18 = 9

So, y = 9.

Thus, C is our answer.

~ an aesthetics lover