# CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Trigonometry

###### CAT Questions | CAT Trigonometry Questions | Heights and Distances CAT Questions

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. $$frac{2}{√3}\\$ m 4. $\frac{6}{√3}\\$ m ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer ##### Method of solving this CAT Question from CAT Geometry - Trigonometry : Relate the flag pole with the building and the man! Let height of the flag pole PQ be x Height of building QR = 7√3 m Height of man AB = √3 Therefore QQ’ = 7√3 – √3 = 6√3 From diagram, tan y° = $\frac{QQ’}{AQ’}\\$ Or tan y° = $\frac{6√3}{√135}\\$ -------$1)
Also, tan (90 – y)° = PQ’/AQ’
Or tan (90 – y)° = $$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. ###### Prepare for CAT 2023 with 2IIM's Daily Preparation Schedule ###### Know all about CAT Exam Syllabus and what to expect in CAT ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2023 Classroom Batches Starting Now! @Gopalapuram ###### Best CAT Coaching in Chennai Introductory offer of 5000/- Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Preparation Online | CAT Geometry - Trigonometry Videos On YouTube #### Other useful sources for Geometry Questions | Trigonometry Questions ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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