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 joing 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
![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.](https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/gr-10-ch-9-010-1563447382.png)
Solution:
Considering ΔABC,
tan 60° = AB/BC
√3 = AB/BC
AB = BC√3 ...(i)
Considering ΔABD,
tan 30° = AB/BD
tan 30° = AB / (CD + BC)
1/√3 = BC√3 / (20 + BC) [from (i)]
20 + BC = BC√3 × √3
20 + BC = 3 × BC
3BC - BC = 20
2BC = 20
BC = 10
Substituting BC = 10 m in Equation (1), we get AB = 10√3 m
Height of the tower AB = 10√3 m
Width of the canal BC = 10 m
☛ Check: NCERT Solutions for Class 10 Maths Chapter 9
Video Solution:
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 joing 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.
Maths NCERT Solutions Class 10 Chapter 9 Exercise 9.1 Question 11
If a TV tower stands vertically on the bank of a canal, and from a point on the other bank directly opposite the tower, if the angle of elevation of the top of the tower is 60°, and 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°, then the height of the tower and the width of the canal are 10√3 m and 10 m respectively.
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