10th Class Mathematics Introduction to Trigonometry Question Bank MCQs - Introduction to Trigonometry

If \[\Delta ABC,\] right angled at B, \[\text{AC}=\text{13 cm},\] \[\text{AB}=\text{5 cm},\] then \[\sin A=\]

A) \[\frac{5}{13}\]

B) \[\frac{5}{12}\]

C) \[\frac{12}{13}\]

D) \[\frac{13}{12}\]

Correct Answer: C

Solution :

[c]\[A{{C}^{2}}=A{{B}^{2}}+B{{C}^{2}}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,B{{C}^{2}}={{(13)}^{2}}-{{(5)}^{2}}=144\,\,\,\,\Rightarrow \,\,\,\,BC=12cm\]

\[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\sin A=\frac{12}{13}\]