# Two direction angles of a vector are given. Find the third direction angle, give

Two direction angles of a vector are given. Find the third direction angle, given ths either obtuse
$$\displaystyle\alpha={60}^{\circ},\beta={50}^{\circ},\gamma\ \text{ is obtuse}$$

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d2saint0
According to given details
$$\displaystyle\alpha={60}^{\circ},\beta={50}^{\circ}$$
Using trigonometry identities
$$\displaystyle{{\cos}^{{2}}\alpha}+{{\cos}^{{2}}\beta}+{{\cos}^{{2}}\gamma}={1}$$
$$\displaystyle{\left({\frac{{{1}}}{{{2}}}}\right)}^{{2}}+{\left({0.6429}\right)}^{{2}}+{{\cos}^{{2}}\gamma}={1}$$
$$\displaystyle{\frac{{{1}}}{{{4}}}}+{0.4132}+{{\cos}^{{2}}\gamma}={1}$$
$$\displaystyle{{\cos}^{{2}}\gamma}={1}-{0.6632}$$
$$\displaystyle{{\cos}^{{2}}\gamma}={0.3368}$$
$$\displaystyle{\cos{\gamma}}=\sqrt{{{0.3368}}}$$
$$\displaystyle\gamma={125.47}^{\circ}$$