A) \[\frac{63}{65}\]
B) \[\frac{60}{65}\]
C) \[\frac{61}{63}\]
D) \[\frac{63}{62}\]
Correct Answer: A
Solution :
Given that A(1,1),B(4,5) and C(6,13), then \[a=BC=\sqrt{4+64}=\sqrt{68}\] \[b=AC=\sqrt{25+144}=13\] \[c=AB=\sqrt{9+16}=5\] \[\therefore \] \[\cos A=\frac{{{b}^{2}}+{{c}^{2}}-{{a}^{2}}}{2bc}\] \[\Rightarrow \] \[\cos A=\frac{169+25-68}{2.13.5}\] \[\Rightarrow \] \[\cos A=\frac{126}{10\times 13}=\frac{63}{65}\]
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