question_answer

From the foot of a pillar of height 10 m the angle of elevation of the top of hill is 60° and from the top of the pillar, the angle of elevation of the top of the hill is 30°. Find the height of the hill.

A)  \[15\sqrt{3}\,m\]                           

B)  \[\frac{15}{\sqrt{3}}\,m\]

C)  \[15\,m\]

D)  \[15\,(\sqrt{3}+1)m\]

Correct Answer: C

Solution :

 Height of hill \[=(10+a)\,m.\] In \[\Delta \,EDA,\]we get \[\tan \,30{}^\circ =\frac{a}{x}\Rightarrow x=a\sqrt{3}\,\,m\]                 ??(i) In \[\Delta ECB,\] \[\tan \,60{}^\circ =\frac{10+a}{x}\] \[\Rightarrow \,\,\sqrt{3}=\frac{10+a}{x}\Rightarrow x=\frac{10+a}{\sqrt{3}}\] \[a\sqrt{3}=\frac{10+a}{\sqrt{3}}\]  (from equation (i)) \[3a=10+a\Rightarrow 2a=10\Rightarrow a=5\text{ }m\] Height of hill \[=\left( 10+5 \right)=\]