Solve the triangle.
-$$\begin{array} { l }
\mathrm { A } = 47 ^ { \circ } \
\mathrm { B } = 42 ^ { \circ } \
\mathrm { a } = 45.2
\end{array}$$
A) $\mathrm { C } = 91 ^ { \circ } , \mathrm { b } = 41.4 , \mathrm { c } = 61.8$
B) $\mathrm { C } = 92 ^ { \circ } , \mathrm { b } = 41.4 , \mathrm { c } = 61.8$
C) $\mathrm { C } = 91 ^ { \circ } , \mathrm { b } = 61.8 , \mathrm { c } = 41.4$
D) $\mathrm { C } = 92 ^ { \circ } , \mathrm { b } = 61.8 , \mathrm { c } = 41.4$

Question

Solve the triangle.
-$$\begin{array} { l } 
\mathrm { A } = 47 ^ { \circ } \
\mathrm { B } = 42 ^ { \circ } \
\mathrm { a } = 45.2
\end{array}$$
A) $\mathrm { C } = 91 ^ { \circ } , \mathrm { b } = 41.4 , \mathrm { c } = 61.8$
B) $\mathrm { C } = 92 ^ { \circ } , \mathrm { b } = 41.4 , \mathrm { c } = 61.8$
C) $\mathrm { C } = 91 ^ { \circ } , \mathrm { b } = 61.8 , \mathrm { c } = 41.4$
D) $\mathrm { C } = 92 ^ { \circ } , \mathrm { b } = 61.8 , \mathrm { c } = 41.4$

Quizplus · Accepted Answer

First, find angle C by subtracting the sum of angles A and B from 180°: $C = 180° - 47° - 42° = 91°$. Then, use the Law of Sines to find sides b and c. The given information and the calculated angle C match option A.

Solve the Triangle A=47∘B=42∘a=45.2\begin{array} { l } \mathrm { A } = 47 ^ { \circ } \\\mathrm { B } = 42 ^ { \circ } \\\mathrm { a } = 45.2\end{array}A=47∘B=42∘a=45.2​

Solve the Triangle $\begin{array} { l } \mathrm { A } = 47 ^ { \circ } \\\mathrm { B } = 42 ^ { \circ } \\\mathrm { a } = 45.2\end{array}$