Question

From the top of a 9 m high building, the angle of elevation of the top of a cable tower is 60º and angle of depression of its foot is 45º. Determine the height of the tower and distance between building and tower. (Use √3 = 1.732)

Answer 1

hh

Let AB be the building and CD be the tower. 

Here tan60° = √3 = h/x

⇒ h = x√3………..(i) 

tan45° = 9/x = 1 

⇒ x = 9 m………….(ii) ( Distance between tower and building) 

Solving (i) & (ii) to get h = 9 × 1.732 = 15.588 m 

Therefore, the height of the tower = h + 9 = 24.588 m.