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

melodykap 2021-08-21 Answered
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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Expert Answer

d2saint0
Answered 2021-08-22 Author has 19123 answers
According to given details
\(\displaystyle\alpha={60}^{\circ},\beta={50}^{\circ}\)
Using trigonometry identities
\(\displaystyle{{\cos}^{{2}}\alpha}+{{\cos}^{{2}}\beta}+{{\cos}^{{2}}\gamma}={1}\)
\(\displaystyle{\left({\frac{{{1}}}{{{2}}}}\right)}^{{2}}+{\left({0.6429}\right)}^{{2}}+{{\cos}^{{2}}\gamma}={1}\)
\(\displaystyle{\frac{{{1}}}{{{4}}}}+{0.4132}+{{\cos}^{{2}}\gamma}={1}\)
\(\displaystyle{{\cos}^{{2}}\gamma}={1}-{0.6632}\)
\(\displaystyle{{\cos}^{{2}}\gamma}={0.3368}\)
\(\displaystyle{\cos{\gamma}}=\sqrt{{{0.3368}}}\)
\(\displaystyle\gamma={125.47}^{\circ}\)
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