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:15
A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.
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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 highway and AB is tower. C is the initial position of the car and D is the position after 6 seconds.
In ΔABD,
AB/DB = tan 60° ⇒ AB/DB = √3 ⇒ BD = AB/√3
In ΔABC,
AB/BC = tan 30°
⇒ AB/(BD + DC) = 1/√3
⇒ AB√3 = BD + DC
⇒ AB = AB/√3 + DC [putting the value of BD]
⇒ AB√3 – AB/√3 = DC
⇒ DC = (3AB – AB)/√3 = 2AB/√3
The time taken to travelled CD (= 2AB/√3) distance = 6 second
Therefore, the speed of the car = distance/time = (2AB/√3)/6 = AB/3√3 m/s
The time taken to travelled BD (= AB/√3) distance = distance/speed = (AB/√3)/ (AB/3√3) = 3 second.
Hence, car will take 3 seconds to reach the foot of the car.