Question

Instructions: Find the missing side lengths. Leave your answers as radicals in simplest form.

Answer 1

Answer:

x = 10$\sqrt{3}$, y = 10

Step-by-step explanation:

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

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

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

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

x = 10$\sqrt{3}$

and

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

2y = 20 ( divide both sides by 2 )

y = 10