If the height of a tower and the distance of the point of observation from its foot, both, are increased by 10%, then the angle of elevation of its top remains unchanged. Write ‘True’ or ‘False’ and justify your answer
Solution:
Given, the height of the tower and the distance of the point of observation from its foot are increased by 10%.
We have to determine if the angle of elevation of its top remains unchanged.
Let AB be the height of tower
Let BC be the distance of the point of observation from its foot.
Let AB = x units and BC = y units
Angle of elevation be θ
In triangle ABC,
tan θ = AB/BC
tan θ = x/y ------------------ (1)
Now, x and y are increased by 10%
x = x + (1/10)x = (1 + 10)/10 x = 11x/10
y = y + (1/10)y = (1 + 10)/10 y = 11y/10
tan θ = (11/10)x / (11/10)y
tan θ = x/y ------------------- (2)
From (1) and (2),
θ remains same
Therefore, the angle of elevation remains unchanged.
✦ Try This: The angle of elevation of the top of a tower from a point on the ground 30m away from the foot of the tower is 30°. The height of the tower is
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8
NCERT Exemplar Class 10 Maths Exercise 8.2 Problem 12
If the height of a tower and the distance of the point of observation from its foot, both, are increased by 10%, then the angle of elevation of its top remains unchanged. Write ‘True’ or ‘False’ and justify your answer
Summary:
The statement “If the height of a tower and the distance of the point of observation from its foot, both, are increased by 10%, then the angle of elevation of its top remains unchanged” is true
☛ Related Questions: