You can use the law of sines: it states that in any triangle, the ratio between the length of a side and the sine of the opposite angle is constant:
[tex] \dfrac{AB}{\sin(C)} = \dfrac{BC}{\sin(A)} = \dfrac{AC}{\sin(B)} [/tex]
We only need one of these equalities. Since B is a right angle, we have [tex] \sin(B)=1 [/tex]. So, since we want to solve the equality for [tex] \sin(C) [/tex], we focus on
[tex] \dfrac{AB}{\sin(C)} = \dfrac{AC}{\sin(B)} \iff \dfrac{24}{\sin(C)} = \dfrac{26}{1}[/tex]
Solving for [tex] \sin(C) [/tex], we have
[tex] \sin(C) = \dfrac{24}{26} = \dfrac{12}{13} [/tex]
