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:8
A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.
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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 BC is Pedestal and AB is 1.6 m high statue.
In ΔBCD,
BC/CD = tan 45° ⇒ BC/CD = 1 ⇒ BC = CD
In ΔACD,
AB+BC/CD = tan 60° ⇒ AB+BC/BC = √3
⇒ 1.6 + BC/BC = √3
⇒ BC + 1.6 = BC√3
⇒ 1.6 = BC (√3 – 1)
⇒ BC = 1.6/(√3-1) × (√3+1)/(√3+1) = 1.6(√3+1)/2
= 0.8(√3+1)
Hence, the height of the pedestal is 0.8(√3+1)m.