The top and bottom of a flag on a building subtend angles of 60° and 30° respectively at a point B which is 48 meter away from the building. Find the height of the flag?

Question: The top and bottom of a flag on a building subtend angles of 60° and 30° respectively at a point B which is 48 meter away from the building. Find the height of the flag?Solution:Let height of building be AC = X and height of flag be CD = h.In ΔDABtan60° = (X + h)/48⇒ √3 = (X + h)/48⇒ X + h = 48√3∴ h = 48√3 - X ..................(1)In ΔCABtan30° = X/48⇒ 1/√3 = X/48∴ X = 48/√3From (1) we get,h = 48√3 - 48/√3= (48 × 3 - 48)/√3= (144 - 48)/√3= 96/√3= (32 × 3)/√3= 32√3