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