Question

The following question find the value of the variables. If your answer is not an integer leave it in simplest radical form

Answer 1

Answer:

option 4

Step-by-step explanation:

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

cos30° = $\frac{\sqrt{3} }{2}$ , sin30° = $\frac{1}{2}$ , then

cos30° = $\frac{adjacent}{hypotenuse}$ = $\frac{x}{20\sqrt{3} }$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

2x = 20$\sqrt{3}$ × $\sqrt{3}$ = 20 × 3 = 60 ( divide both sides by 2 )

x = 30

and

sin30° = $\frac{opposite}{hypotenuse}$ = $\frac{y}{20\sqrt{3} }$ = $\frac{1}{2}$ ( cross- multiply )

2y = 20$\sqrt{3}$ ( divide both sides by 2 )

y = 10$\sqrt{3}$