Question

# A statue, $$1.6$$ m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is $$\displaystyle { 60 }^{ \circ }$$ and from the same point the angle of elevation of the top of the pedestal is $$\displaystyle { 45 }^{ \circ }$$. Find the height of the pedestal.

Solution

## Let $$AB$$ be the length of the statue and $$BC$$ be the length of the pedestal.In $$\triangle BCD$$, $$\dfrac{BC}{CD} = \tan 45^o$$ $$\therefore BC=CD$$In $$\triangle ACD$$, $$\tan 60^o=\dfrac {AC}{CD}$$$$\dfrac{AB+BC}{CD}=\sqrt{3}$$$$BC+1.6=\sqrt{3}CD$$$$BC+1.6=\sqrt{3}BC$$$$BC=\dfrac{1.6}{\sqrt{3}-1}$$$$BC=\dfrac{1.6(\sqrt{3}+1)}{(\sqrt{3}-1)(\sqrt{3}+1)}$$$$=\dfrac{1.6(\sqrt{3}+1)}{(\sqrt{3})^2-(1)^2}=\dfrac{1.6(\sqrt{3}+1)}{2}$$$$=0.8(\sqrt{3}+1)$$ mMathematicsRS AgarwalStandard X

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