Answer:
x = 4[tex]\sqrt{3}[/tex], y = 8[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the tangent ratio in the right triangle and the exact value
tan30° = [tex]\frac{\sqrt{3} }{3}[/tex] , then
tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{12}[/tex] = [tex]\frac{\sqrt{3} }{3}[/tex] ( cross- multiply )
3x = 12[tex]\sqrt{3}[/tex] ( divide both sides by 3 )
x = 4[tex]\sqrt{3}[/tex]
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Using Pythagoras' identity in the right triangle
y² = x² + 12² = (4[tex]\sqrt{3}[/tex] )² + 144 = 48 + 144 = 192 ( take square root of both sides )
y = [tex]\sqrt{192}[/tex] = [tex]\sqrt{64(3)}[/tex] = 8[tex]\sqrt{3}[/tex]
