A vertical pole and a vertical tower are on the same level ground in such a way that, from the top of the pole, the angle of elevation of the top of the tower is 60° and the angle of depression of the bottom of the tower is 30°. If the height of the pole is 24 m, then find the height of the tower (in m).

Answer: Option C

Solution

Answer: Option C

Solution:

$$\begin{array}{rl}& \text{In }\Delta ABD,\\ & \tan 30^{\circ }=\frac{P}{B}\\ & \frac{1}{\sqrt{3}}=\frac{24}{BD}\\ & BD=24\sqrt{3}\\ & BD=AE=24\sqrt{3}\\ & \text{In }\Delta AEC,\\ & \tan 60^{\circ }=\frac{P}{B}\\ & \sqrt{3}=\frac{CE}{AE}\\ & \sqrt{3}=\frac{CE}{24\sqrt{3}}\\ & CE=24\times 3=72\\ & \text{Height of tower }CD=CE+ED\\ & =72+24=96\text{ cm}\end{array}$$