From the window of a house, the angle of elevation of the top of a flag is 60° and the angle of depression of its base is 30°. If the horizontal distance of the flag from the house is 6m, then find the height of the flag.

Correct option is C

Given:

- Horizontal distance from the house to the flagpole (d) = 6 m
- Angle of elevation to the top of the flag (θ₁) = 60°
- Angle of depression to the base of the flag (θ₂) = 30°

Let:
- h_top = height of the flag's top above the house window
- h_base = height of the flag's base below the house window
- Total height of the flag = h = h_top + h_base

Step 1: Calculate h_top (height from the house window to the top of the flagpole)
Using tan θ = opposite / adjacent:
tan(60°) = h_top / 6
√3 = h_top / 6
h_top = 6√3 m

Step 2: Calculate h_base (height from the house window to the base of the flagpole)
Using tan(30°):
tan(30°) = h_base / 6
1/√3 = h_base / 6
h_base = 6 / √3 = 2√3 m

Step 3: Total height of the flagpole
h = h_top + h_base
h = 6√3 + 2√3 = 8√3 m