A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building
Solution:
Let's represent the situation using a diagram according to the given question.
Distance walked towards the building RQ = PR - PQ
Trigonometric ratio involving AP, PR and ∠R and AP, PQ and ∠Q is tan θ [Refer the diagram to visualise AP, PR and PQ]
In ΔAPR
tan R = AP/PR
tan 30° = 28.5/PR
1/√3 = 28.5/PR
PR = 28.5 × √3 m
In ΔAPQ
tan Q = AP/PQ
tan 60° = 28.5/PQ
√3 = 28.5/PQ
PQ = 28.5 / √3 m
Therefore,
PR - PQ = 28.5√3 - 28.5/√3
= 28.5 (√3 - 1/√3)
= 28.5 ((3 - 1)/√3)
= 28.5 (2/√3)
= 57/√3
= (57 × √3)/(√3 × √3)
= (57√3)/3
= 19√3 m
The distance walked by the boy towards the building is 19√3 m.
☛ Check: NCERT Solutions Class 10 Maths Chapter 9
Video Solution:
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building
Maths NCERT Solutions Class 10 Chapter 9 Exercise 9.1 Question 6
Summary:
If a 1.5 m tall boy is standing at some distance from a 30 m tall building, the angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building, then the distance he walked towards the building is 19√3 m.
☛ Related Questions:
- From a point on the ground,the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively.Find the height of the tower.
- A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.
- The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.
- Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles