Answer:
see explanation
Step-by-step explanation:
Using the sine ratio in right Δ ACD and the exact value
sin30° = [tex]\frac{1}{2}[/tex]
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AD}{AC}[/tex] = [tex]\frac{y}{150}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2y = 150 ( divide both sides by 2 )
y = 75
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Using the tangent ration in right Δ ABD and the exact value
tan60° = [tex]\sqrt{3}[/tex]
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AD}{BD}[/tex] = [tex]\frac{y}{z}[/tex] = [tex]\frac{75}{z}[/tex] = [tex]\sqrt{3}[/tex] ( cross- multiply )
[tex]\sqrt{3}[/tex] z = 75 ( divide both sides by [tex]\sqrt{3}[/tex] )
z = [tex]\frac{75}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] = [tex]\frac{75\sqrt{3} }{3}[/tex] = 25[tex]\sqrt{3}[/tex]
