What is the measurement (using tangent) of an angle that has an adjacent side of 8, an opposite side of 9, and a hypotenuse of 10?
You can find the size of the angles, but this is not a right-angle triangle, and you can not use the terminology you have used.
The cosine rule states that
$\displaystyle \displaystyle \begin{align*} c^2 &= a^2 + b^2 - 2ab\cos{C} \\ \cos{C} &= \frac{a^2 + b^2 - c^2}{2ab} \end{align*}$