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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.


Solution

The statement is false.
To understand the fact of this question, consider the following example

I. A tower 23 m high casts a shadow 2m long on the ground, then the Sun’s elevation is 60

In ΔACB,tan θ=ABBC=232

tan θ=3=tan 60

θ=60



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

In ΔAPB,tan θ=ABPB=ABPC+CB

tan θ=234+2=236

tan θ=33.33=333

=13=tan 30

θ=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.

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