Question

At a point on level ground, the angle of elevation of a vertical tower is, found to be α such that tan α = 1/3. After walking 100 m towards the tower, the angle of elevation β becomes such that tan β = 3/4. Find the height of the tower.

The angles of depression of the top and bottom of a 6 m tall building from the top of a multi-storeyed building are 30° and 45° respectively. Find the height of the multi-storeyed building and the distance between the two buildings. (Use √3 = 1·73)

As observed from the top of a 100 m high lighthouse from the sea-level, the angles of depression of two ships are found to be 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. [Use √3 = 1.732]

Basant and Vinod lives in a housing society in Dwarka, New Delhi. There are two building in their housing society. The first building is 8 meter tall. One day, both of them were just trying to guess the height of the other multi-storeyed building. Vinod said that it might be a 45 degree angle from the bottom of our building to the top of multi-storeyed building so the height of the building and distance from our building to this multi-storeyed building will be same. Then, both of them decided to estimate it using some trigonometric tools. Let's assume that the first angles of depression of the top and bottom of an 8 m tall building from top of a multi-storeyed building are 30° and 45°, respectively.