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A lower subtends an angle of 30° at a point on the same level as its foot. At a second point h metres above the first, the depression of the foot of the tower is 60°. The height of the tower is.

A. $\frac{h}{2} m$ B. $\sqrt{3} h m$ C. $\frac{h}{3} m$ D. $\frac{h}{\sqrt{3}} m$ Answer: Option C
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Solution(By Apex Team)

A lower subtends an angle of 30° at a point on the same level as its foot. image Let CD is the tower and A is a point such that the angle of elevation of C is 30° B is and their point h m high of A and angle of depression of D is 60° $\begin{array}{l}\text{AB}=h\text{ metre}\\ \text{Let CD}=\text{h}\ \text{metre}\\ \text{and AD}=x\\ \text{Now in right }\triangle\ \text{ABD,}\\ \tan\theta=\frac{AB}{AD}\\ \Rightarrow\tan60^{\circ}=\frac{h}{x}\\ \Rightarrow\sqrt{3}=\frac{h}{x}\\ \Rightarrow x=\frac{h}{\sqrt{3}}\ldots\ldots\text{ (i) }\\ \text{Similarily in right }\triangle\ \text{ACB,}\\ \tan30^{\circ}=\frac{CD}{AD}\\ \Rightarrow\frac{1}{\sqrt{3}}=\frac{H}{x}\\ \Rightarrow x=\sqrt{3}H\ldots\ldots.\\ \text{ From (i) and (ii) }\\ \sqrt{3}H=\frac{h}{\sqrt{3}}\\ H=\frac{h}{\sqrt{3}\times\sqrt{3}}=\frac{h}{3}\\ \therefore\text{Height of tower}\\ =\frac{h}{3}\end{array}$