Solve the triangle.
-$$\mathrm { A } = 52 ^ { \circ } , \mathrm { B } = 63 ^ { \circ } , \mathrm { a } = 8$$
A) $\mathrm { C } = 65 ^ { \circ } , \mathrm { b } \approx 9 , \mathrm { c } \approx 9.2$
B) $\mathrm { C } = 25 ^ { \circ } , \mathrm { b } \approx 7.1 , \mathrm { c } \approx 8.1$
C) $\mathrm { C } = 65 ^ { \circ } , \mathrm { b } \approx 7.1 , \mathrm { c } \approx 8.1$
D) $\mathrm { C } = 65 ^ { \circ } , \mathrm { b } \approx 9 , \mathrm { c } \approx 8.1$

Question

Quizplus · Accepted Answer

To solve the triangle, first find angle C using the fact that the sum of angles in a triangle is 180 degrees: $C = 180^\circ - A - B = 180^\circ - 52^\circ - 63^\circ = 65^\circ$. Then, use the Law of Sines to find sides b and c: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$. Solving for b and c gives $b \approx 9$ and $c \approx 9.2$.

Solve the Triangle A=52∘,B=63∘,a=8\mathrm { A } = 52 ^ { \circ } , \mathrm { B } = 63 ^ { \circ } , \mathrm { a } = 8A=52∘,B=63∘,a=8

Solve the Triangle $\mathrm { A } = 52 ^ { \circ } , \mathrm { B } = 63 ^ { \circ } , \mathrm { a } = 8$