The shadow of a tower standing on a level ground is found to be 40 m
Trigonometry (10)The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun’s altitude is 30° than when it was 60°. Find the height of the tower.
Answer
$$ \text{In } \triangle ABC, \tan 60^0 = \frac{h}{x} \Rightarrow h = \sqrt{3}x $$
$$ \text{In } \triangle ABD, \tan 30^0 = \frac{h}{x+40} \Rightarrow x + 40 = \sqrt{3}h $$
Getting x = 20 m
$$ h = 20 \sqrt{3} m \text{ (Height of tower)} $$
- Exam Year: 2023
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