Question

Find the value of each variable

Answer 1

Answer:

x = 10$\sqrt{2}$ , y = 10$\sqrt{6}$

Step-by-step explanation:

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

cos60° = $\frac{1}{2}$ , sin60° = $\frac{\sqrt{3} }{2}$ , then

cos60° = $\frac{adjacent}{hypotenuse}$ = $\frac{x}{20\sqrt{2} }$ = $\frac{1}{2}$ ( cross- multiply )

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

x = 10$\sqrt{2}$

and

sin60° = $\frac{opposite}{hypotenuse}$ = $\frac{y}{20\sqrt{2} }$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

2y = 20$\sqrt{2}$ × $\sqrt{3}$ = 20$\sqrt{6}$ ( divide both sides by 2 )

y = 10$\sqrt{6}$