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).
Answer & explanation
Correct answer: option 3
⇒ 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.