The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60° and the angle of elevation of the top of the second tower from the foot of the first tower is 30°. Find the distance between the two towers and also the height of the other tower
Solution:
Given, the angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60°
The angle of elevation of the top of the second tower from the foot of the first tower is 30°
We have to find the distance between the two towers and also the height of the other tower.
Let BQ be the first tower with height 30 m
Angle of elevation, ∠QAB = 60°
Let PA be the second tower with height h m
Angle of elevation, ∠PBA = 30°
AB is the distance between the two towers.
In triangle AQB,
tan 60° = QB/AB
By trigonometric ratio of angles,
tan 60° = √3
So, √3 = 30/AB
AB = 30/√3 m
AB = 3(10)/√3
AB = 10√3 m
Therefore, the distance between two towers is 10√3 m.
In triangle APB,
By using pythagorean theorem,
tan 30° = AP/AB
By trigonometric ratio of angles,
tan 30° = 1/√3
So, 1/√3 = AP/(30/√3)
AP = (30/√3)/√3
AP = 30/3
AP = 10 m
Therefore, the height of the second tower is 10 m.
✦ Try This: The angle of elevation of the top of a cell phone tower from the foot of a high apartment is 60° and the angle of depression of the foot of the tower from the top of the apartment is 30°. If the height of the apartment is 50 m, find the height of the cell phone tower. According to radiations control norms, the minimum height of a cell phone tower should be 120 m. State if the height of the above mentioned cell phone tower meets the radiation norms.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8
NCERT Exemplar Class 10 Maths Exercise 8.4 Problem 13
The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60° and the angle of elevation of the top of the second tower from the foot of the first tower is 30°. Find the distance between the two towers and also the height of the other tower
Summary:
The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60° and the angle of elevation of the top of the second tower from the foot of the first tower is 30°. The distance between the two towers is 10√3 m and also the height of the other tower is 10 m
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