The angle of elevation of the top of a tower is 30°. If the height of the tower is doubled, then the angle of elevation of its top will also be doubled. Write ‘True’ or ‘False’ and justify your answer
Solution:
Given, angle of elevation of the top of a tower is 30°
We have to determine if the height of the tower is doubled, the angle of elevation of its top will also be doubled i.e., θ = 60°
Let AC be the height of the tower
AC = h units
BC = x units
Angle of elevation = 30°
tan 30° = AC/BC
By using trigonometric ratio of angles,
tan 30° = 1/√3
1/√3 = h/x ------------ (1)
Now, the height of the tower is doubled.
So, PR = 2h units
RQ = x units
Let the angle of elevation be θ
tan θ = PR/RQ
tan θ = 2h/x ---------------- (2)
Substituting (1) in (2),
tan θ = 2(1/√3)
tan θ = 2/√3
tan θ = 1.15
θ = tan⁻¹(1.15)
θ = 49°< 60°
Therefore, the angle of elevation is not doubled.
✦ Try This: The angles of elevation of the top of a rock from the top and foot of a 100 m high tower are respectively 30° and 45°. Find the height of the rock.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8
NCERT Exemplar Class 10 Maths Exercise 8.2 Problem 11
The angle of elevation of the top of a tower is 30°. If the height of the tower is doubled, then the angle of elevation of its top will also be doubled. Write ‘True’ or ‘False’ and justify your answer
Summary:
The statement “The angle of elevation of the top of a tower is 30°. If the height of the tower is doubled, then the angle of elevation of its top will also be doubled” is false
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