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
Cuemath is one of the world's leading math learning platforms that offers LIVE 1-to-1 online math classes for grades K-12. Our mission is to transform the way children learn math, to help them excel in school and competitive exams. Our expert tutors conduct 2 or more live classes per week, at a pace that matches the child's learning needs.
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.
☛ Related Questions:
- A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30° (see Fig. 9.12). Find the height of the tower and the width of the canal.
- From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.
- As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.
- A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After some time, the angle of elevation reduces to 30° (see Fig. 9.13). Find the distance travelled by the balloon during the interval.