Question

From a point 31 meters from the base of a telephone pole the angle of elevation to a worker on the pole is 35 degrees. The angle of elevation to the top of the pole is 68 degrees. Find the distance from the worker to the top of the pole.

Answer 1

51.02 metres

Explanation:

The pictorial representation of the problem is attached.

We are required to find the distance from the worker to the top of the pole, |DA| in the diagram.

In Triangle ABC

`Tan 68^\circ =(|AB|)/(|BC|)\\Tan 68^\circ =(|AB|)/(31)\\|AB|=31 X Tan 68^\circ=72.73m`

In Triangle BCD

`Tan 35^\circ =(|BD|)/(|BC|)\\Tan 35^\circ =(|BD|)/(31)\\|BD|=31 X Tan 35^\circ=21.71m`

The distance, |DA| =|AB|-|BD|

=72.73-21.71

=51.02 metres

The distance from the worker to the top of the pole is 51.02 metres.