**Applications of Trigonometry Heights and Distances Chapter 9 Exercise 9.1 Question 10**

**10. ** Two poles of equal heights are standing opposite 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 and , respectively. Find the height of the poles and the distances of the point from the poles.

**Solution:**

It is given that poles (AB and ED) are of equal height.

** It is also given that BD = 80 m**

**Let CD = x m**

**And, let BC = (80 - x) m**

In , we have

m **(1)**

In , we have

**(2)**

**We have ED = AB because both the poles are of equal height.**

Therefore,

m

**BC=80-x = 80-60=20 m**

Putting value of **x** in equation **(1)**, we get

m

**Therefore, Distances of the point C from the poles are 60 m and 20 m.**

**And, the height of poles is** m