Question

The angle of elevation of the top of a tower from a point 100m away from the base of the tower is 45°. The angle of elevation of the top of the flag staff mounted on the top of the tower is 60°. The height of the flag staff is.......... (Use √3 =1.73)​

Answer 1

The height of the flag staff is 73 m

Explanation:

Let H₁ be the height of the building.

Since the angle of elevation of the top of the tower is 45° from a point 100 m away from the base of the tower,

From tan45° = H₁/100

H₁ = 100tan45° = 100 m

Let H₂ be the height of the building plus flag staff.

Since the angle of elevation of the top of the flag staff is 60° from the same point 100 m away from the base of the tower,

From tan60° = H₂/100

H₂ = 100tan60°

= 100√3

= 100 × 1.73

= 173 m.

So, the height of the flag staff is h = H₂ - H₁

= 173 m - 100 m

= 73 m.

So, the height of the flag staff is 73 m