check the picture below.
[tex]\bf cos(\theta)=\cfrac{adjacent}{hypotenuse}\quad cos(CAB)=\cfrac{5}{13}\implies \measuredangle CAB=cos^{-1}\left( \frac{5}{13} \right)
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\textit{that means that }\measuredangle hAC=\cfrac{cos^{-1}\left( \frac{5}{13} \right)}{2}\impliedby \textit{one of the halves}[/tex]
now, notice, for the angle hAC, the hypotenuse is hA, and the adjacent side is CA, therefore,
[tex]\bf cos(\theta)=\cfrac{adjacent}{hypotenuse}\qquad cos(hAC)=\cfrac{5}{hA}\implies hA=\cfrac{5}{cos(hAC)}
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hA=\cfrac{5}{cos\left[ \frac{cos^{-1}\left( \frac{5}{13} \right)}{2} \right]}[/tex]
make sure your calculator is in Degree mode, if you need the angle in degrees.
