Question

Find the missing side lengths leave your answerss as radicals

Answer 1

Answer:

x = 8, y = 4

Step-by-step explanation:

To find x use the sine ratio in the right triangle and the exact value

sin60° = $\frac{\sqrt{3} }{2}$ , thus

sin60° = $\frac{opposite}{hypotenuse}$ = $\frac{4\sqrt{3} }{x}$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

x × $\sqrt{3}$ = 8$\sqrt{3}$ ( divide both sides by $\sqrt{3}$ )

x = 8

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To find y use the tangent ratio in the right triangle and the exact value

tan60° = $\sqrt{3}$ , thus

tan60° = $\frac{opposite}{adjacent}$ = $\frac{4\sqrt{3} }{y}$ = $\sqrt{3}$ ( multiply both sides by y )

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

y = 4