# 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. $$frac{5√3}{2}\\$ 2. 5√3 3. Both A and B 4. Can’t be determined ## 2IIM : Best Online CAT Coaching #### Signup and sample 5 classes for free ## Best CAT Coaching in Chennai #### Batches filling fast. Starts Sat, June 8th, 2019 ### Explanatory Answer ##### Method of solving this CAT Question from CAT Geometry - Trigonometry : Since the directions are unknown, we are left with two different possibilities! Case 1 : tan 30° = $\frac{h}{x}\\$ ∴ h = $\frac{x}{√3}\\$ tan 60° = $\frac{h}{$10-x$}$ => h =$10 – x) √3
∴ (10 – x) √3 = $$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. ###### Best Online CAT CoachingSignup and sample5 classes for free Signup Now! ###### Already have an Account? ###### CAT Coaching in ChennaiEnroll at 29000/- Next Weekend Batch Starts Sat, June 29th, 2019 ###### Best CAT Coaching in ChennaiEarly Bird discount of 7000 Personalised attention, Small batch sizes. ## 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, 10-C, Kalinga Colony, Bobbili Raja Salai K.K.Nagar, Chennai. India. Pin - 600 078 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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