Question

Find the missing side lengths. Leave your answer as radicals in simplest form.

Answer 1

Answer:

x = 4$\sqrt{2}$, y = 2$\sqrt{6}$

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin30° = $\frac{1}{2}$ , then

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

x = 4$\sqrt{2}$

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Using the tangent ratio in the right triangle and the exact value

tan30° = $\frac{1}{\sqrt{3} }$ , then

tan30° = $\frac{opposite}{adjacent}$ = $\frac{2\sqrt{2} }{y}$ = $\frac{1}{\sqrt{3} }$ ( cross- multiply )

y = 2$\sqrt{6}$