NCERT Solutions for Class 10 Maths Chapter 1
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:205
Questions No:14
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° Find the distance travelled by the balloon during the interval.
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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 CD is 1.2m high girl and FG is the distance travelled by balloon.
In ΔACE,
AE/CE = tan 60°
⇒ (AF – EF)/CE = √3
⇒ (88.2 – 1.2)/CE = √3
⇒ 87/CE = √3 ⇒ CE = 87/√3 = 87√3/3 = 29√3
In ΔBCG,
BG/GC = tan 30° ⇒ 88.2 – 1.2/CG = 1/√3
⇒ 87/CG = 1/√3 ⇒ CG = 87√3
Distance travelled by balloon = EG = CG – CE = 87√3 – 29√3 = 58√3
Hence, the distance travelled by balloon is 58√3m.