Question

A house has a window `h' meters above the ground. Across the street from this house, there is a tall pole. The angles of elevation and depression of the top and bottom of this pole from the window are $\theta$ and $\Phi$ respectively. Determine the height of the pole.

• A. h (1 - tan θ cot Φ)
• B. h (1 + tan θ)
• C. h (1 - cot Φ)
• D. h (1 - cot θ cot Φ)
• E. h (1 + tan θ cot Φ)

Answer 1

The correct option is E

h (1 + tan θ cot Φ)

Note that d = h cot $\Phi$ and h' = d tan $\theta$ = h tan $\theta$ cot $\Phi$

Thus, the height of the pole is h + h' = h (1 + tan $\theta$ cot $\Phi$)