Question

Find the values of x and y.

Answer 1

Answer:

x = 4$\sqrt{6}$ , y = 8$\sqrt{2}$

Step-by-step explanation:

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

sin45° = $\frac{\sqrt{2} }{2}$

let the altitude of the outer triangle be h ( common to both right triangles )

sin45° = $\frac{opposite}{hypotenuse}$ = $\frac{h}{8}$ = $\frac{\sqrt{2} }{2}$ ( cross- multiply )

2h = 8$\sqrt{2}$ ( divide both sides by 2 )

h = 4$\sqrt{2}$

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

tan30° = $\frac{1}{\sqrt{3} }$ , then

tan30° = $\frac{opposite}{adjacent}$ = $\frac{h}{x}$ = $\frac{4\sqrt{2} }{x}$ = $\frac{1}{\sqrt{3} }$ ( cross- multiply )

x = 4$\sqrt{6}$

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

sin30° = $\frac{1}{2}$ , then

sin30° = $\frac{h}{y}$ = $\frac{4\sqrt{2} }{y}$ = $\frac{1}{2}$ ( cross- multiply )

y =8$\sqrt{2}$

Answer 2

Answer:

........

Step-by-step explanation: