Question

Find the missing side lengths. leave your answers as radicals in simplest form.

Answer 1

Answer:

x = 4 , y = 2

Step-by-step explanation:

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

sin60° = $\frac{\sqrt{3} }{2}$ and tan60° = $\sqrt{3}$ , then

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

x $\sqrt{3}$ = 4$\sqrt{3}$ ( divide both sides by $\sqrt{3}$ )

x = 4

and

tan60° = $\frac{opposite}{adjacent}$ = $\frac{2\sqrt{3} }{y}$ = $\sqrt{3}$ ( multiply both sides by y )

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

y = 2