Question
From a point on the ground, the angle of elevation of the top of a tower is 45 degrees. After moving 20 m away from the tower, the angle becomes 30 degrees. Find the height of the tower.
Solution
ATQ, Let the initial distance from tower be x m. Since angle = 45 degrees, height = x After moving 20 m away, distance = x + 20 Now, tan 30 = height/(x + 20) 1/√3 = x/(x + 20) x + 20 = x√3 20 = x(√3 - 1) x = 20/(√3 - 1) = 20(√3 + 1)/2 = 10(√3 + 1) Height = x = 10(√3 + 1) m Answer: A. 10(1 + √3) m
More Height and Distance Questions
- From a watch tower of 205 m height, the angles of depression of two cliffs in a horizontal line through the base of the tower are 45° and 30°. Find the dis...
- There are two houses of the same height on both sides of a 30-meter wide road. From a point on the road, elevation angles of the houses are 30° and 60&...
- The angle of depression of a point on the ground as seen from the top of a tower, 25 feet high, is 45°. Find the distance of the point on the ground from t...
- The shadow of a pole 24m long is 56m. Then what will be the approximate shadow of building 40m high at the similar situation?
- A pole 6 m high casts a shadow 2√3 m long on the ground. Find the angle of elevation
- From a point situated at some distance from the base of a pillar, the angle of elevation of the top of the pillar is found to be 45 degrees. After walking ...
- The height of a conical tent is 9m. A vertical pole of 6m height is placed 4 m away from its centre such that it touches the surface. Find the slant height...
- From a point 30 m away, the angle of elevation of top of tower is 45°. Find height of tower.
- The two buildings are 100m apart. From the top of the first building, which is 60m tall, the angle of depression to the top of the second building is 45 de...
- There is a fire in the building. A man on the top of the building see a Fire brigade van coming towards it. If it takes 8 minutes for the angle of depressi...
Relevant for Exams:
