NCERT Solutions for Class 10 Maths Chapter 9
Important NCERT Questions
SOME APPLICAT IONS OF TRIGONOMETRY
(Height and Distance)
NCERT Books for Session 2022-2023
CBSE Board and UP Board Others state Board
EXERCISE 9.1
Page No:204
Questions No:11
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° Find the height of the tower and the width of the canal.
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Get here all the solutions of class 10 Maths Exercise 9.1
NCERT Solutions for class 10 Maths Exercise 9.1 all questions in Hindi Medium
Let AB is TV tower and BC is width of the canal. In ΔABC,
AB/BC = tan 60° ⇒ AB/BC = √3
⇒ BC = AB√3
In ΔABD,
AB/BD = tan 30° ⇒ AB/(BC+CD) = 1/√3
⇒ AB/(AB/√3+CD) = 1/√3 [Putting the value of BC]
⇒ AB√3/(AB + 20√3) = 1/√3 ⇒ 3AB = AB + 20√3 ⇒ 2AB = 20√3 ⇒AB = 10√3
Therefore, BC = AB/√3 = 10√3/√3= 10
Hence, the height of the tower is 10√3m and the width of tower is 10m.