CAT Practice : Trigonometry

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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

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More questions from Trigonometry

Trigonometry..........
The text passage contains a mathematical question related to trigonometry, specifically about finding the height of a hot air balloon based on the angles observed by two people. The passage also provides a detailed solution and the correct answer.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
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

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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

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More questions from Trigonometry

Trigonometry..........
user
The text passage contains a mathematical question related to trigonometry, specifically about finding the height of a hot air balloon based on the angles observed by two people. The passage also provides a detailed solution and the correct answer.

TYPE: SINGLE_QUESTION_WITH_ANSWER