If the length of the shadow of a tower is increasing, then the angle of elevation of the sun is also increasing. Write ‘True’ or ‘False’ and justify your answer
Solution:
We have to determine if the length of the shadow of a tower is increasing, then the angle of elevation of the sun is also increasing.
Consider a pole of height 2√3 m cast a shadow of 2 m, then the sun’s elevation is θ
tan θ = opposite/adjacent
tan θ = 2√3/2
tan θ = √3
θ = tan⁻¹(√3)
We know that tan 60° = √3
So, θ = 60°
Now, shadow increases to 4 m, then the angle of elevation is θ
tan θ = 2√3/(2 + 4)
tan θ = 2√3/6
tan θ = √3/3
tan θ = 1/√3
θ = tan⁻¹(1/√3)
We know that tan 30° = 1/√3
So, θ = 30°
It is clear from the two cases that the angle of elevation decreases when the length of the shadow increases.
✦ Try This: The shadow of a tower, when the angle of elevation of the sun is 45°, is found to be 10 m longer than when it was 60°. Find the height of the tower.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8
NCERT Exemplar Class 10 Maths Exercise 8.2 Problem 7
If the length of the shadow of a tower is increasing, then the angle of elevation of the sun is also increasing. Write ‘True’ or ‘False’ and justify your answer
Summary:
The statement “If the length of the shadow of a tower is increasing, then the angle of elevation of the sun is also increasing” is false
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