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.

19

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.