The angle of elevation of the top of a tower from a certain point is 30°. If the observer moves 20 meters towards the tower, the angle of elevation of the top increases by 15°. Find the height of the tower
Solution:
Given, the angle of elevation of the top of a tower from a certain point is 30°
If the observer moves 20 m towards the tower, the angle of elevation of the top increases by 15°
We have to find the height of the tower.
Let AB be the tower
C and D be the point of observation
∠BCA = 30°
Given, CD = 20 m
When the observer moves from the point C to D the angle of elevation increases by 15°
So, ∠BDA = 30° + 15°
∠BDA = 45°
In triangle BAD,
tan 45° = AB/AD
1 = h/AD
AD = h ----------------- (1)
In triangle BAC,
By pythagorean theorem,
tan 30° = AB/AC
1/√3 = h/AC
We know that AC = CD + AD
AC = 20 + h
Now, 1/√3 = h/(20 + h)
20 + h = √3(h)
On simplification,
√3h - h = 20
h(√3 - 1) = 20
h(1.732 - 1) = 20
h(0.732) = 20
h = 20/0.732
h = 27.3 m
Therefore, the height of the tower is 27.3 m
✦ Try This: The length of the shadow of a tower standing on level ground is found to be 2x meters longer when the sun’s elevation is 30° than when it was 45°. The height of the tower in meters is
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8
NCERT Exemplar Class 10 Maths Exercise 8.4 Problem 3
The angle of elevation of the top of a tower from a certain point is 30°. If the observer moves 20 meters towards the tower, the angle of elevation of the top increases by 15°. Find the height of the tower
Summary:
The angle of elevation of the top of a tower from a certain point is 30°. If the observer moves 20 meters towards the tower, the angle of elevation of the top increases by 15°. The height of the tower is 27.3 m
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