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.

Solution

## The statement is false. To understand the fact of this question, consider the following example I. A tower 2√3 m high casts a shadow 2m long on the ground, then the Sun’s elevation is 60∘ In ΔACB,tan θ=ABBC=2√32 ⇒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=2√34+2=2√36 ⇒tan θ=√33.√33=33√3 ⇒=1√3=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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