Question

Two poles of equal heights are standing opposite to each other on either side of the road which is 80 m wide. From a point between them on the road the angles of elevation of the top of the poles are 60° and 30° respectively. Find the height of the poles and the distances of the point from the poles.

Answer 1

Answer:

see this attachment hope it helps ❤️

Answer 2

To find the height of the poles we have to use trigonometry ratio. The distance between the point from the poles can also be calculated using trigonometric ratio.

Explanation:

Let the height of the poles be ‘h’. (both poles have same height).

Pole1 makes an angle 60 Deg and pole 2 makes an angle 30 deg.

Total distance between the poles is 80 m.  

Let the distance between first pole and point be ‘x’

The distance between point and second pole = ’80-x’

Here in Triangle ABC,

Tan 60 = h/x

     √3  = h/x      or   h = √3.x    ---------------- 1.

Now in triangle ECD,

Tan 30 = h/(80-x)

1/(√3)  = h/(80-x)    or     h = (80-x)/(√3)  ------------------2.

Equating 1 and 2, we get

√3.x    = (80-x)/(√3)  

Or √3. √3 . x = 80 –x

 Or 3x = 80 –x

3x + x = 80    or 4x = 80

So, x = 80/4 = 20m

So the distance between the first pole and the point is 20m, and the distance between point and second pole is 80-20 = 60m.

Now  calculating the height of the poles

We have,    h = √3.x = 1.732 x 20 = 34.64 m.

The height of the pole is 34.64m.

(figure attached).