Answer:
[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {a}^{2} + {5}^{2} = {13}^{2} \\ {a}^{2} + 25 = 169 \\ {a}^{2} = 169 - 25 \\ {a}^{2} = 144 \\ a = 12[/tex]
[tex] \sin(B) = \frac{Opposite}{hypotenuse} = \frac{5}{13} \\ \\ \\ \cos(B) = \frac{adjacent}{hypotenuse} = \frac{12}{13} \\ \\ \\ \tan(B) = \frac{opposite}{adjacent} = \frac{5}{12} [/tex]
