2018 · Q59
From a height of h units, a man observes the angle of elevation as α and angle of depression as β of the top and the bottom respectively of a tower of height H (> 4h). To what further height should he climb so that the values of angle of elevation and angle of depression get interchanged for the top and bottom of the tower?
Elementary MathematicsTrigonometry
- AH - h units
- BH - 2h units
- CH - 3h units
- DH - 4h units
Explanation
Originally tanα = (H − h)/d and tanβ = h/d, where d is the horizontal distance. After climbing x with the angles interchanged, the depression angle becomes α, so tanα = (h + x)/d. Thus h + x = H − h, i.e. x = H − 2h, option (B). (H > 4h keeps all quantities positive.)