Answer:
x = 16, y = 8[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the sine ratio in the right triangle and the exact value
sin30° = [tex]\frac{1}{2}[/tex] , then
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{8}{x}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
x = 16
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Using Pythagoras' identity in the right triangle
y² + 8² = 16²
y² + 64 = 256 ( subtract 64 from both sides )
y² = 192 ( take the square root of both sides )
y = [tex]\sqrt{192}[/tex] = [tex]\sqrt{64(3)}[/tex] = 8[tex]\sqrt{3}[/tex]
