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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