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:13
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.
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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 75 m high lighthouse and C and D are the two ships.
In ΔABC,
AB/BC = tan 45° ⇒ 75/BC = 1
⇒ BC = 75
In ΔABD,
AB/BD = tan 30°
⇒ 75/(BC + CD) = 1/√3
⇒ 75/(75 + CD) = 1/√3
⇒ 75 + CD = 75√3
⇒ CD = 75(√3 – 1)
Hence, the distance between the two ships is 75(√3 – 1).