## If the length of the shadow of a tower is increasing, then the angle of elevation of the sun is also increasing. Is it True or False…

Question

If the length of the shadow of a tower is increasing, then the angle of elevation of the sun is also increasing.
Is it True or False…?????

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1 month 2021-08-15T09:45:08+00:00 2 Answers 0 views 0

Note: When the sun’s elevation decreases the Shadow will become lengthy…

U can see it at sunrise or sunset

## False..

### To understand the fact of this question, consider the following example.

1. A tower 23m high casts a shadow 2m long on the ground, then the Sun’s elevation is 60 degree. (fig. 1)

In ΔACB, tanθ = AB/BC = 23/2

tanθ = 3 = tan60 degree

Therefore, θ = 60 degree

2. A same height of tower casts a shadow 4m more from preceding points, then the Sun’s elevation is 30 degree. (fig. 2)

On ΔAPB, tanθ = AB/PB = AB/PC+CB

tanθ = 23/4+2 = 23/6

tanθ = 3/3 * 3/3 = 3/33

tanθ = 1/3 = tan30 degree

Therefore , θ = 30 degree

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 :

### False,

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