The top of a 15 metre high tower makes an angle of elevation of 60° with the bottom of an electric pole and angle of elevation of 30° with the top of the pole. What is the height of electric pole ?
A. 5 meters
B. 8 meters
C. 10 meters
D. 12 meters
E. None of these
Answer: Option C
Solution(By Examveda Team)
Let AB be the tower and CD be the electric pole.
Then, $$\angle ACB = {60^ \circ },$$ $$\angle EDB = {30^ \circ }$$ and AB = 15 m
Let CD = h
Then, BE = (AB - AE) = (AB - CD) = (15 - h)
$$\eqalign{ & \frac{{AB}}{{AC}} = \tan {60^ \circ } = \sqrt 3 \cr & \Rightarrow AC = \frac{{AB}}{{\sqrt 3 }} = \frac{{15}}{{\sqrt 3 }} \cr & {\text{And, }}\frac{{BE}}{{DE}} = \tan {30^ \circ } = \frac{1}{{\sqrt 3 }} \cr & \Rightarrow DE = \left( {BE \times \sqrt 3 } \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = \sqrt 3 \left( {15 - h} \right) \cr & {\text{So, }}AC = DE \cr & \Rightarrow \frac{{15}}{{\sqrt 3 }} = \sqrt 3 \left( {15 - h} \right) \cr & \Rightarrow 3h = \left( {45 - 15} \right) \cr & \Rightarrow h = 10{\text{ m}} \cr} $$
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