CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Trigonometry

The question is from CAT Geometry - Trigonometry. This is about Heights and distances. We need to find out the ratio of the heights of the tower which are placed in a hexagon. 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 3: Consider a regular hexagon ABCDEF. There are towers placed at B and D. The angle of elevation from A to the tower at B is 30 degrees, and to the top of the tower at D is 45 degrees. What is the ratio of the heights of towers at B and D?

1. 1:√3
2. 1:2√3
3. 1:2
4. 3:4√3

Explanatory Answer

Method of solving this CAT Question from CAT Geometry - Trigonometry : When you look at your reflection through a mirror, the image is at a distance equal to the distance between mirror and you. Now, think about what this has to with trigonometry.

Let the hexagon ABCDEF be of side ‘a’. Line AD = 2a. Let towers at B and D be B’B and D’D respectively.

From the given data we know that ∠B´AB = 30^° and ∠D´AB = 45^°. Keep in mind that the Towers B’B and D´D are not in the same plane as the hexagon.

In Triangle B’AB,
Tan∠B´AB = B´AB = \\frac{B'B}{AB}\\) = \\frac{1}{3}\\)
=> B’B = \\frac{a}{√3}\\)
In Triangle D´AD, tan ∠D´AD = \\frac{D'D}{AD}\\) = 1
=> D’D = 2a
Ratio of heights = \\frac{1}{√3}\\) or \\frac{1}{2√3}\\)
Answer choice (B)

The question is "What is the ratio of heights?"

Hence, the answer is 1:2√3

Choice B is the correct answer.