| Direction: Q. 11 to 15 |
| Three friends - Sanjeev, Amit and Digvijay are playing hide and seek in a park. Sanjeev and Amit hide in the shrubs and Digvijay have to find both of them. If the positions of three friends are at A, B and C respectively as shown in the figure and forms a right angled triangle such that \[\text{AB}=\text{9 m},\] \[\text{BC}=3\sqrt{3}\text{ m}\] and \[\angle B=90{}^\circ \]. |
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| Based on the above information, give the answer of the following questions: |
A) \[30{}^\circ \]
B) \[45{}^\circ \]
C) \[60{}^\circ \]
D) None of these
Correct Answer: A
Solution :
| We have, \[AB=9m,\] \[BC=3\sqrt{3}m\] |
| In \[\Delta ABC,\]we have |
| \[\tan A=\frac{BC}{AB}=\frac{3\sqrt{3}}{9}=\frac{1}{\sqrt{3}}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\tan A=\tan 30{}^\circ \,\,\,\,\,\,\Rightarrow \,\,\,\,\,\,\,\,\angle A=30{}^\circ \] .(1) |
| So, option [a] is correct. |
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