CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Trigonometry

The question is from CAT Geometry - Trigonometry. This is about Heights and Distances. Our task is to find out the time taken to reach the tower by comparing the given details. Trigonometry is an important topic for CAT Preparation for the CAT Exam. Trigonometric ideas can be completely opposite, as in, some questions test lot of common sense with direction, heights and distances, while others could test you on identities. CAT exam could test one on both these fronts. Make sure you master both in CAT - Trigonometry.

Question 9: A man standing on top of a tower sees a car coming towards the tower. If it takes 20 minutes for the angle of depression to change from 30° to 60°, what is the time remaining for the car to reach the tower?

1. 20√3 minutes
2. 10 minutes
3. 10√3 minutes
4. 5 minutes

Explanatory Answer

Method of solving this CAT Question from CAT Geometry - Trigonometry : Does the angle of depression increase as we go nearby?

From the figure:-

tan 30° = \\frac{h}{(a+b)}\\)
tan 60° = \\frac{h}{b}\\)
∴ \\frac{(a+b)}{√3}\\) = b√3
=> a + b = 3b
=> 2b = a
=> b = \\frac{a}{2}\\)

Now since the car takes 20 minutes to travel a distance
Time taken to travel b = \\frac{a}{2}\\) distance = \\frac{20}{2}\\) = 10 minutes

The question is "What is the time remaining for the car to reach the tower?"

Hence, the answer is 10 minutes

Choice B is the correct answer.