Given data:
The given measurement of angle C is 90 degrees.
The given value of cos(B) =5/13.
The sum of all angles of triangle is,
[tex]\begin{gathered} \angle A+\angle B+\angle C=180^{\circ} \\ \angle A+\angle B+90^{\circ}=180^{\circ} \\ \angle A+\angle B=90^{\circ} \\ \angle B=90^{\circ}-\angle A \end{gathered}[/tex]Substitute the above value in the given expression.
[tex]\begin{gathered} \cos (90^{\circ}-A)=\frac{5}{13} \\ \sin A=\frac{5}{13} \end{gathered}[/tex]Thus, the correct answer is sin(A), so the third option is correct.
