The observer's height is 1.5 m, standing 28.5 m away from the chimney. The angle of elevation from her eyes to the top of the chimney is 45°.
The angle is measured from the observer's eye level, not from the ground.
The total height of the chimney consists of two parts:
- Height above eye level (h)
- Observer's eye level height (1.5 m)
From the observer's eyes, a right triangle is formed with:
- Horizontal distance = 28.5 m
- Angle of elevation = 45°
- Opposite side = h (height above eye level)
tan(45°)=28.5h
Since tan(45°)=1:
1=28.5h
h=28.5 m
Total height of chimney = Height above eye level + Observer's height
Total height =28.5+1.5
Total height =30 m
Therefore, the height of the chimney is 30 m.