Solve the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.
-$$\begin{array} { l }
\mathrm { B } = 15.4 ^ { \circ } \
\mathrm { C } = 100.2 ^ { \circ } \
\mathrm { b } = 22.4
\end{array}$$
A) $\mathrm { A } = 64.4 ^ { \circ } , \mathrm { a } = 78.1 , \mathrm { c } = 85$
B) $\mathrm { A } = 62.4 ^ { \circ } , \mathrm { a } = 83 , \mathrm { c } = 76.1$
C) $\mathrm { A } = 64.4 ^ { \circ } , \mathrm { a } = 76.1 , \mathrm { c } = 83$
D) $\mathrm { A } = 62.4 ^ { \circ } , \mathrm { a } = 85 , \mathrm { c } = 78.1$

Question

Solve the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.
-$$\begin{array} { l } 
\mathrm { B } = 15.4 ^ { \circ } \
\mathrm { C } = 100.2 ^ { \circ } \
\mathrm { b } = 22.4
\end{array}$$
A) $\mathrm { A } = 64.4 ^ { \circ } , \mathrm { a } = 78.1 , \mathrm { c } = 85$
B) $\mathrm { A } = 62.4 ^ { \circ } , \mathrm { a } = 83 , \mathrm { c } = 76.1$
C) $\mathrm { A } = 64.4 ^ { \circ } , \mathrm { a } = 76.1 , \mathrm { c } = 83$
D) $\mathrm { A } = 62.4 ^ { \circ } , \mathrm { a } = 85 , \mathrm { c } = 78.1$

Quizplus · Accepted Answer

To solve the triangle, first find angle A using the fact that the sum of angles in a triangle is 180 degrees: $A = 180^\circ - B - C = 180^\circ - 15.4^\circ - 100.2^\circ = 64.4^\circ$. Then, use the Law of Sines to find sides a and c. Since the provided information and the correct angle calculation match option C, it is the correct choice.

Solve the Triangle B=15.4∘C=100.2∘b=22.4\begin{array} { l } \mathrm { B } = 15.4 ^ { \circ } \\\mathrm { C } = 100.2 ^ { \circ } \\\mathrm { b } = 22.4\end{array}B=15.4∘C=100.2∘b=22.4​

Solve the Triangle $\begin{array} { l } \mathrm { B } = 15.4 ^ { \circ } \\\mathrm { C } = 100.2 ^ { \circ } \\\mathrm { b } = 22.4\end{array}$