From the top of a 195-m high cliff, the angles of depression of the top and bottom of a tower are 30° and 60°, respectively. Find the height of the tower (in m).

130

⇒ Let RT = (195 - a)m and PQ = b m

Now for triangle RST

⇒ tan \({30}^\circ\) = \(\frac{195 - a}{b}\)

⇒ b = (195 - a)\(\sqrt { 3}\)

And for triangle PQR

⇒ tan \({60}^\circ\) = \(\frac{195 }{b}\)

⇒ b = \(\frac{195 }{√3}\)

Now,

⇒ b = (195 - a)\(\sqrt { 3}\) = \(\frac{195 }{√3}\)

⇒ 195 = 585 - 3a

⇒ 3a = 390

⇒ a = 130m

Therefore, height of tower is 130m.