text: CAT Practice : Trigonometry
  
  You are here: Home  CAT Questionbank   CAT Quant  Geometry: Trigonometry  Question 8
  Max and Min value of the given expression
  
  Height and Distances
  
  Q.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. $\frac{5}{2}√3$
  2. 5√3
  3. Both A and B
  4. Can’t be determined
  
  Choice C. Both A and B
  
  Detailed Solution
  
  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
  
  Correct Answer: Both A and B
  
  Our Online Course, Now on Google Playstore!
  
  Fully Functional Course on Mobile
  
  All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.
  
  Cache Content for Offline Viewing
  
  Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!
  
  More questions from Trigonometry
  
  Trigonometry..........