Question

Question 7
Write ‘True’ or ‘False’ and justify your answer in each of the following:
If the length of the shadow of a tower is increasing, then the angle of elevation of the Sun is also increasing.

Answer 1

The statement is false.
To understand the fact of this question, consider the following example
I. A tower $2\sqrt{3}m$ high casts a shadow 2m long on the ground, then the Sun’s elevation is ${60}^{\circ }$

In $\Delta ACB,tan\theta =\frac{AB}{BC}=\frac{2\sqrt{3}}{2}$

$\Rightarrow tan\theta =\sqrt{3}=tan{60}^{\circ }$

$\therefore \theta ={60}^{\circ }$



II. A same height of tower casts a shadow 4m more from preceding point, then the Sun’s elevation is ${30}^{\circ }$.

In $\Delta APB,tan\theta =\frac{AB}{PB}=\frac{AB}{PC+CB}$

$\Rightarrow tan\theta =\frac{2\sqrt{3}}{4+2}=\frac{2\sqrt{3}}{6}$

$\Rightarrow tan\theta =\frac{\sqrt{3}}{3}.\frac{\sqrt{3}}{3}=\frac{3}{3\sqrt{3}}$

$\Rightarrow =\frac{1}{\sqrt{3}}=tan{30}^{\circ }$

$\therefore \theta =30$

Hence, we conclude from above two examples that if the length of the shadow of a tower is increasing, then the angle of elevation of the Sun is decreasing.

Alternate Method:

We know that, if the elevation moves towards the tower, it increases and if its elevation moves away from the tower, it decreases. Hence, if the shadow of a tower is increasing, then the angle of elevation of the Sun is not increasing.