A vertical pole and a vertical tower are on the same level of 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 tower is 76 m, then find the height (in m) of the pole.
Answer & explanation
Correct answer: option 3
Let the height of the pole (AB) = CD = a m
Height of ED = (76 - a) m
In triangle ACD, tan \({30}^\circ\) = \(\frac{CD}{AD}\)
⇒ \(\frac{1}{√3}\) = \(\frac{a}{AD}\)
⇒ AD = √3a ..(1.)
In triangle AED, tan \({60}^\circ\) = \(\frac{ED}{AD}\)
⇒ √3 = \(\frac{76 - a}{√3a}\)
⇒ 76 - a = 3a
⇒ 3a + a = 76
⇒ 4a = 76
⇒ a = 19,
Therefore, the height of the pole is 19m.