A man observes the angle of elevation of the top of the tower to be 45°. He walks towards it in a horizontal line through its base. On covering 20 m the angle of elevation changes to 60°. Find the height of the tower correct to 2 significant figures.

Topic: Quadratic equations

Previous-year question practice database

Answer

Solution diagram

Exam answer

Let tower height = h m. Let nearer distance = x m. Initial distance = x+20 m.

tan45° = h/(x+20) ⇒ h=x+20.

tan60° = h/x ⇒ h=√3x.

So: √3x = x+20 x = 20/(√3−1) = 10(√3+1) ≈ 27.32.

h=x+20 ≈47.32 m.

To two significant figures:

Answer: 47 m.

Explanation

Use tanθ = tower height/horizontal distance at the two observation points.