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y is [tex]8\sqrt{3}[/tex]. This is because in a 30-60-90 triangle, the side facing the 30° is always half of the side facing the 90°


x is always √3 times y, so x=24. Therefore, the answer is the second answer choice.

Answer:

x = 24 , y = 8√3 .

Step-by-step explanation:

Given : 30- 60- 90 angled triangle.

To find : Solve for x and y.

Solution : We have given : opposite angle = y

Hypotenuses = 16√3.

Adjacent side = x.

By the 30- 60- 90 angled triangle rule : Adjacent side is √3 times of opposite side and hypotenuses is 2 times of opposite side,

Then ,

Hypotenuses = 2 * opposite side.

Plug hypotenuses = 2√3.

16√3 = 2 * y .

On dividing  by 2 both sides.

8√3 = y.

Adjacent side = √3 * opposite side.

x = √3 * y

x = √3 * 8√3 .

x = 8 * 3

x = 24.

Therefore, x = 24 , y = 8√3 .

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