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 & explanation
Correct answer: option 3
⇒ In triangle ABC
⇒ tan \({30}^\circ\) = \(\frac{24}{BC}\)
⇒ \(\frac{1}{√3}\) = \(\frac{24}{BC}\)
⇒ BC = 24\(\sqrt {3 }\)m
Now,
⇒ In triangle ADE
⇒ tan \({60}^\circ\) = \(\frac{ED}{24√3}\)
⇒ \(\sqrt {3 }\) = \(\frac{ED}{24√3}\)
⇒ ED = 24\(\sqrt {3 }\) x \(\sqrt {3 }\) = 24 x 3 = 72m
As DC = AB
⇒ EC = ED + DC
⇒ EC = 72 + 24
⇒ EC = 96m
Therefore, the height of the tower is 96m.