# 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 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles

**Solution:**

Let us consider the two poles of equal heights as AB and DC and the distance between the poles as BC.

From a point O, between the poles on the road, the angle of elevation of the top of the poles AB and CD are 60° and 30° respectively.

Trigonometric ratio involving angles, distance between poles and heights of poles is tan θ.

Let the height of the poles be x

Therefore AB = DC = x

In ΔAOB,

tan 60° = AB/BO

√3 = x / BO

BO = x / √3 ....(i)

In ΔOCD,

tan 30° = DC / OC

1/√3 = x / (BC - OB)

1/√3 = x / (80 - x/√3) [from (i)]

80 - x/√3 = √3x

x/√3 + √3x = 80

x (1/√3 + √3) = 80

x (1 + 3) / √3 = 80

x (4/√3) = 80

x = 80√3 / 4

x = 20√3

Height of the poles x = 20√3 m.

Distance of the point O from the pole AB

BO = x/√3

= 20√3/√3

= 20

Distance of the point O from the pole CD

OC = BC - BO

= 80 - 20

= 60

The height of the poles is 20√3 m and the distance of the point from the poles is 20 m and 60 m.

**☛ Check: **NCERT Solutions Class 10 Maths Chapter 9

**Video Solution:**

## 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 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles.

Maths NCERT Solutions Class 10 Chapter 1 Exercise 9.1 Question 10

**Summary:**

If two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide, and from a point between them on the road, the angles of elevation of the top of the poles are 60° and 30° respectively, then the height of the poles are 20√3 m and the distances of the point from the poles is 20 m and 60 m respectively.

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