Solve the triangle. Find the angles α and β first.
-$$\mathrm { a } = 8 , \mathrm {~b} = 6 , \mathrm { c } = 4$$
A) $\alpha = 104.5 ^ { \circ } , \beta = 46.6 ^ { \circ } , \gamma = 28.9 ^ { \circ }$
B) $\alpha = 104.5 ^ { \circ } , \beta = 28.9 ^ { \circ } , \gamma = 46.6 ^ { \circ }$
C) $\alpha = 46.6 ^ { \circ } , \beta = 28.9 ^ { \circ } , \gamma = 104.5 ^ { \circ }$
D) $\alpha = 46.6 ^ { \circ } , \beta = 104.5 ^ { \circ } , \gamma = 28.9 ^ { \circ }$

Question

Quizplus · Accepted Answer

Using the Law of Cosines, we can find the angles α and β:$$\alpha = \cos^{-1}\left(\frac{b^2 + c^2 - a^2}{2bc}\right) = \cos^{-1}\left(\frac{6^2 + 4^2 - 8^2}{2(6)(4)}\right) = 104.5^\circ$$$$\beta = \cos^{-1}\left(\frac{a^2 + c^2 - b^2}{2ac}\right) = \cos^{-1}\left(\frac{8^2 + 4^2 - 6^2}{2(8)(4)}\right) = 46.6^\circ$$

Solve the Triangle a=8, b=6,c=4\mathrm { a } = 8 , \mathrm {~b} = 6 , \mathrm { c } = 4a=8, b=6,c=4

Solve the Triangle $\mathrm { a } = 8 , \mathrm {~b} = 6 , \mathrm { c } = 4$