| In figure, \[\text{AD}=\text{4}\,\text{cm},\] \[\text{BD}=\text{3 cm}\] and \[\text{CB}=\text{12 cm},\]then the value of \[\cot \theta \] is:(CBSE 2016) |
 |
A) \[\frac{5}{12}\]
B) \[\frac{12}{5}\]
C) \[\frac{7}{5}\]
D) \[\frac{5}{7}\]
Correct Answer: B
Solution :
| [b] In right-angled \[\Delta ADB.\] |
| \[A{{B}^{2}}=B{{D}^{2}}+A{{D}^{2}}\] |
| \[={{(3)}^{2}}+{{(4)}^{2}}\] (By Pythagoras theorem) |
| \[=9+16=25\] |
| \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,AB=5cm\] |
| Now, in right-angled \[\Delta ABC\] |
| \[\cot \theta =\frac{BC}{AB}=\frac{12}{5}\] |
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