Direction cosines for an angle >90?

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I hope this question is not stupid but I seem to be missing avery basic point. In the following calculation to find the angle alpha it appears the Cos = Adj/Hyp is used. However, I thought this was only allowed for right angled triangles? From this picture, the angle 'a' seems to be >90.

There is a similar example in advanced engineering mathematics by Stroud under the vector analysis area that poses the same issue. Am I missing something very basic?

Wikipedia direction of cosines

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There is a way to extend the definition of the trigonometric ratios to cover "angles" more than $90°.$

One way is to use the coordinates of the unit circle in rectangular coordinates. The cosine is the abscissa, and the corresponding ordinate is the sine of the angle determined by the radius and the $x$-axis.