The angles of elevation of the top of a tower from two points on the ground at distances 32 m and 18 m from its base and in the same straight line with it are complementary. The height (in m) of the tower is ______.
Answer & explanation
Correct answer: option 3
⇒ In triangle PQR
⇒ tan A = \(\frac{PQ}{18}\) ..(1.)
⇒ In triangle PSQ
⇒ tan(90 - A) = \(\frac{PQ}{32}\)
⇒ cot A = \(\frac{32}{PQ}\)
⇒ tan A = \(\frac{32}{PQ}\) ..(2.)
Equating 1 and 2,
⇒ \(\frac{PQ}{18}\) = \(\frac{32}{PQ}\)
⇒ \( {PQ }^{2 } \) = 32 x 18 = 576
⇒ PQ = 24m
Therefore, height of the tower is 24 m.