Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
1.2k views
in Trigonometry by (44.3k points)

A straight highway leads to the foot of a tower. A man standing on 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 form this point.

1 Answer

+1 vote
by (58.8k points)
selected by
 
Best answer

Draw a figure based on given instructions:

In the figure, AC be the tower and AB be the canal.

Let AC = h, AB = x and BD = y

From right △CBA:

cot 60° = x/h

1/√3 = x/h

or x = h/√3

From right △CAD:

cot 30° = (x+y)/h

√3 = (x+y)/h

y = 2h/√3

Since y distance is covered in 6 seconds, then x distance is covered in 6x/y seconds

Substituting the values of x and y, we get

6x/y = (6h/√3)/ (2h/√3)

= 3

Therefore, time taken by the car to reach the foot of the tower form this point is 3 seconds.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...