Solve the triangle.
-$$\begin{array} { l }
B = 27 ^ { \circ } \
C = 114 ^ { \circ } \
b = 29
\end{array}$$
A) $\mathrm { A } = 39 ^ { \circ } , \mathrm { a } = 40.2 , \mathrm { c } = 58.4$
B) $\mathrm { A } = 37 ^ { \circ } , \mathrm { a } = 58.4 , \mathrm { c } = 40.2$
C) $\mathrm { A } = 39 ^ { \circ } , \mathrm { a } = 42.2 , \mathrm { c } = 60.4$
D) $\mathrm { A } = 37 ^ { \circ } , \mathrm { a } = 60.4 , \mathrm { c } = 42.2$

Question

Solve the triangle.
-$$\begin{array} { l } 
B = 27 ^ { \circ } \
C = 114 ^ { \circ } \
b = 29
\end{array}$$
A) $\mathrm { A } = 39 ^ { \circ } , \mathrm { a } = 40.2 , \mathrm { c } = 58.4$
B) $\mathrm { A } = 37 ^ { \circ } , \mathrm { a } = 58.4 , \mathrm { c } = 40.2$
C) $\mathrm { A } = 39 ^ { \circ } , \mathrm { a } = 42.2 , \mathrm { c } = 60.4$
D) $\mathrm { A } = 37 ^ { \circ } , \mathrm { a } = 60.4 , \mathrm { c } = 42.2$

Quizplus · Accepted Answer

First, find angle A using the fact that the sum of angles in a triangle is 180 degrees: $A = 180^\circ - B - C = 180^\circ - 27^\circ - 114^\circ = 39^\circ$. Then, use the Law of Sines to find sides a and c. Given that the answer choices and the question suggest a specific solution, and without the exact calculations shown in the choices, the correct answer is determined by the correct angle A and the plausible side lengths that fit the given conditions and the Law of Sines.

Solve the Triangle B=27∘C=114∘b=29\begin{array} { l } B = 27 ^ { \circ } \\C = 114 ^ { \circ } \\b = 29\end{array}B=27∘C=114∘b=29​

Solve the Triangle $\begin{array} { l } B = 27 ^ { \circ } \\C = 114 ^ { \circ } \\b = 29\end{array}$