A 2 m tall boy is 30 m away from a tower. The angle of elevation of the top of the tower from his eye is 45°. What is the height of the tower?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 32 m
The angle of elevation is measured from the boy’s eye, 2 m above the ground, so the right triangle gives only the part of the tower above eye level: \(\tan\theta=\frac{\text{height above the eye}}{\text{distance}}\). The boy’s height is then added.
Height above eye level \(=30\times\tan45^\circ=30\times1=30\) m
Height of the tower \(=30+2=32\) m
Tip: 30 m (Option 1) is only the part of the tower above the boy’s eye; whenever the angle is taken from an observer’s eye, add the observer’s height.