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

###### CAT Questions | CAT Trigonometry Questions | Heights and Distance CAT Questions

The question is from CAT Geometry - Trigonometry. This question is about Heights and Distances. Our task is to find out the height at which a ballon is flying given the angles made by two observers. 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 8: Ram and Shyam are 10 km apart. They both see a hot air balloon passing in the sky making an angle of 60° and 30° respectively. What is the height at which the balloon could be flying?

1. $$frac{5√3}{2}\\$ 2. 5√3 3. Both A and B 4. Can’t be determined ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer ##### Method of solving this CAT Question from CAT Geometry - Trigonometry : Since the directions are unknown, we are left with two different possibilities! Case 1 : tan 30° = $\frac{h}{x}\\$ ∴ h = $\frac{x}{√3}\\$ tan 60° = $\frac{h}{$10-x$}$ => h =$10 – x) √3
∴ (10 – x) √3 = $$frac{x}{√3}\\$ => 30 – 3x = x =)x = $\frac{30}{4}\\$= $\frac {15}{2}\\$ => ∴h = $\frac{15}{$2√3$})= $$frac {$5√3$}{2}$ Case 2 : tan 60° = $\frac{h}{x}\\$ =) h = $\frac{x}{√3}\\$ Also, tan 30° = $\frac{h}{$10-x$}$ => h = $\frac{$10-x$}{√3}$ =) 3x – x = 10 => x = 5 H = 5√3 The question is "What is the height at which the balloon could be flying" ##### Hence, the answer is Both A and B Choice C is the correct answer. ###### Prepare for CAT 2022 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 2022 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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