An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45°. What is the height of the chimney?
Correct: A
Let the height of the observer be h_o = 1.5 m. Let the distance from the chimney be d = 28.5 m.
Let the height of the chimney be H. The observer's eyes are at a height of 1.5 m from the ground.
Let the horizontal distance from the observer's eye level to the chimney be the same as the distance from the base, which is 28.5 m.
Let 'x' be the height of the chimney above the observer's eye level.
In the right-angled triangle formed by the observer's eye, the point directly above the observer on the chimney, and the top of the chimney:
tan 45° = x / 28.5.
Since tan 45° = 1:
1 = x / 28.5, so x = 28.5 m.
The total height of the chimney H is the height of the observer plus 'x':
H = h_o + x = 1.5 m + 28.5 m = 30 m.