The angle of elevation of the top of a tower as observed from a point on the ground is α and on moving a meters towards the tower, the angle of elevation is β. Prove that the height of the tower is atanαtanβtanβ−tanα.
Answer:
- The situation given in the question is represented by the image given below.
Let AB be a tower of height h. - In the right-angled triangle ABC, we have
- In the right-angled triangle , we have
- Now, let us substitute the value of in .
- Thus, the height of the tower is