question_answer

If \[\alpha \,\sin A=5\] and \[7\,\cos ec\,A=6\,\sec \,A\], then the value of a is

A) \[\frac{46}{45}\]

B) \[\frac{46}{7}\]

C) \[\frac{49}{46}\]

D) None of these

Correct Answer: B

Solution :

\[\sin A=\frac{5}{\alpha }\] and \[7\,\cos ecA=6\,\sec \,A\]

Let the \[\Delta ABC\] be a right triangle.

\[\angle B=90{}^\circ\]

\[\sin A=\frac{5}{\alpha }\]

\[BC=5k,\,AC=\alpha k\]

\[7\,\cos ec\,A=6\,\sec \,A\]

\[7\times \frac{AC}{BC}=6\,\frac{AC}{AB}\]

\[\frac{7}{5k}=\frac{6}{AB}\]

\[AB=\frac{30k}{7}\]

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

\[{{\left( \frac{30}{7}k \right)}^{2}}+{{\left( 5k \right)}^{2}}{{\alpha }^{2}}{{k}^{2}}\]

\[\sqrt{\frac{900+49\times 25}{49}}=\alpha\]

\[\Rightarrow \,\,\,\alpha =\sqrt{\frac{2125}{49}}=\frac{46}{7}\]    (approx)