Solve the triangle. Find the angles α and β first.
-$a = 8 , b = 13 , c = 17$
A) $\alpha = 25 ^ { \circ } , \beta = 47.5 ^ { \circ } , \gamma = 107.5 ^ { \circ }$
B) $\alpha = 29 ^ { \circ } , \beta = 45.5 ^ { \circ } , \gamma = 105.5 ^ { \circ }$
C) $\alpha = 27 ^ { \circ } , \beta = 47.5 ^ { \circ } , \gamma = 105.5 ^ { \circ }$
D) no triangle

Question

Quizplus · Accepted Answer

Using the Law of Cosines, we can find the angles α and β:cos(α) = (b^2 + c^2 - a^2) / (2bc) = (13^2 + 17^2 - 8^2) / (2 * 13 * 17) = 0.7887α = cos^-1(0.7887) = 27°cos(β) = (a^2 + c^2 - b^2) / (2ac) = (8^2 + 17^2 - 13^2) / (2 * 8 * 17) = 0.6820β = cos^-1(0.6820) = 47.5°The sum of the angles in a triangle is 180°, so γ = 180° - α - β = 180° - 27° - 47.5° = 105.5°.

Solve the Triangle a=8,b=13,c=17a = 8 , b = 13 , c = 17a=8,b=13,c=17

Solve the Triangle $a = 8 , b = 13 , c = 17$