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 height of a flag pole which is on top of a building. 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 16: A flag is hoisted on top of a building of height 7√3 m. A man of height √3 m,standing on the ground, sees the top and bottom of the flag pole at 2 different angles of elevation that are found to be complementary. If the man is standing √135 m away from the building, find the height of the flag pole.

1. 3√3 m
2. 1.5√3 m
3. \\frac{2}{√3}\\) m
4. \\frac{6}{√3}\\) m

Explanatory Answer

Method of solving this CAT Question from CAT Geometry - Trigonometry : Relate the flag pole with the building and the man!

Let height of the flag pole PQ be x
Height of building QR = 7√3 m
Height of man AB = √3
Therefore QQ’ = 7√3 – √3 = 6√3

From diagram, tan y° = \\frac{QQ’}{AQ’}\\)
Or tan y° = \\frac{6√3}{√135}\\) ------- (1)
Also, tan (90 – y)° = PQ’/AQ’
Or tan (90 – y)° = \\frac{(x + QQ’)}{√135}\\)
But tan (90 – y)° = cot y°
Therefore cot y = \\frac{x + 6√3}{√135}\\)
or tan y = \\frac{√135}{x + 6√3}\\) --------(2)

Equating (1) and (2), we get
\\frac{6√3}{√135}\\) = \\frac{√135}{x + 6√3}\\)
6√3x + 108 = 135
6√3x = 27
x = \\frac{9}{2√3}\\) or x = 1.5√3

The question is "To find the height of the flag pole."

Hence, the answer is 1.5√3

Choice B is the correct answer.