question_answer

If O is at the origin, OA is along the negative\[x-\]axis and\[(-40,9)\]is point on OB, then the value of \[\sin \,\angle AOB\] is

A)  5/16                                     

B)  9/40

C)  9/41                     

D)         19/41

E)  None of these

Correct Answer: C

Solution :

Now, \[O{{B}^{2}}=O{{A}^{2}}+A{{B}^{2}}\] \[={{40}^{2}}+{{9}^{2}}=1681\] \[\Rightarrow \]               \[OB=41\] \[\therefore \]  \[sin\angle AOB=\frac{AB}{OB}=\frac{9}{41}\]