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 ______.

24

⇒ 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.