Find the height of a tower standing on level ground whose shadow is 40 m when the Sun's altitude is 45°.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 40 m
The tower, its shadow and the sun’s ray form a right triangle, with the sun’s altitude as the angle at the tip of the shadow, so \(\tan\theta=\frac{\text{height}}{\text{shadow}}\).
\(\displaystyle \tan45^\circ=\frac{h}{40}\)
\(\tan45^\circ=1\), so \(h=40\) m
Tip: At an altitude of \(45^\circ\) the shadow is as long as the object is tall, so the answer can be read off at once.