Solve the triangle. Find the angles  and  first.
-$$\mathrm { a } = 8 , \mathrm {~b} = 8 , \mathrm { c } = 7$$
A) $\alpha = 64.1 ^ { \circ } , \beta = 51.8 ^ { \circ } , \gamma = 64.1 ^ { \circ }$
B) $\alpha = 51.8 ^ { \circ } , \beta = 64.1 ^ { \circ } , \gamma = 64.1 ^ { \circ }$
C) $\alpha = 64.1 ^ { \circ } , \beta = 64.1 ^ { \circ } , \gamma = 51.8 ^ { \circ }$
D) $\alpha = 65.1 ^ { \circ } , \beta = 65.1 ^ { \circ } , \gamma = 49.8 ^ { \circ }$

Question

Quizplus · Accepted Answer

Given a triangle with sides a = 8, b = 8, and c = 7, it is an isosceles triangle (since a = b). Therefore, angles opposite equal sides are equal ($\alpha = \beta$). Using the Law of Cosines to find one of the angles, and knowing the sum of angles in a triangle is 180 degrees, we can determine that $\alpha$ and $\beta$ are equal and larger than $\gamma$, which corresponds to the side with a different length.

Solve the Triangle a=8, b=8,c=7\mathrm { a } = 8 , \mathrm {~b} = 8 , \mathrm { c } = 7a=8, b=8,c=7

Solve the Triangle $\mathrm { a } = 8 , \mathrm {~b} = 8 , \mathrm { c } = 7$