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[tex] \cos( \alpha ) = \frac{5}{13} \\ [/tex]
[tex] \tan( \alpha ) = \frac{12}{5} \\ [/tex]
[tex] \tan( \alpha ) = \frac{ \sin( \alpha ) }{ \cos( \alpha ) } \\ [/tex]
[tex] \frac{12}{5} = \frac{ \sin( \alpha ) }{ \frac{5}{13} } \\ [/tex]
Multiply sides by 5 / 13
[tex] \frac{5}{13} \times \frac{12}{5} = \frac{5}{13} \times \frac{ \sin( \alpha ) }{ \frac{5}{13} } \\ [/tex]
[tex] \frac{5 \times 12}{5 \times 13} = \sin( \alpha ) \\ [/tex]
[tex] \frac{12}{13} = \sin( \alpha ) \\ [/tex]
[tex] \sin( \alpha ) = \frac{12}{13} \\ [/tex]
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