Find the missing parts of the triangle.
-$$\begin{array} { l }
\mathrm { B } = 104.3 ^ { \circ } \
\mathrm { a } = 298 \mathrm {~cm} \
\mathrm {~b} = 1324 \mathrm {~cm}
\end{array}$$
If necessary, round angles the nearest tenth and side lengths to the nearest $\mathrm { cm }$.
A) $\mathrm { A } = 12.6 ^ { \circ } , \mathrm { C } = 63.1 ^ { \circ } , \mathrm { c } = 1218 \mathrm {~cm}$
B) no such triangle
C) $\mathrm { A } = 15.6 ^ { \circ } , \mathrm { C } = 60.1 ^ { \circ } , \mathrm { c } = 1218 \mathrm {~cm}$
D) $\mathrm { A } = 63.1 ^ { \circ } , \mathrm { C } = 12.6 ^ { \circ } , \mathrm { c } = 1218 \mathrm {~cm}$

Question

Find the missing parts of the triangle.
-$$\begin{array} { l } 
\mathrm { B } = 104.3 ^ { \circ } \
\mathrm { a } = 298 \mathrm {~cm} \
\mathrm {~b} = 1324 \mathrm {~cm}
\end{array}$$
If necessary, round angles the nearest tenth and side lengths to the nearest $\mathrm { cm }$.
A) $\mathrm { A } = 12.6 ^ { \circ } , \mathrm { C } = 63.1 ^ { \circ } , \mathrm { c } = 1218 \mathrm {~cm}$
B) no such triangle
C) $\mathrm { A } = 15.6 ^ { \circ } , \mathrm { C } = 60.1 ^ { \circ } , \mathrm { c } = 1218 \mathrm {~cm}$
D) $\mathrm { A } = 63.1 ^ { \circ } , \mathrm { C } = 12.6 ^ { \circ } , \mathrm { c } = 1218 \mathrm {~cm}$

Quizplus · Accepted Answer

Using the Law of Sines, we can find angle A by setting up the ratio $\frac{a}{\sin A} = \frac{b}{\sin B}$. Substituting the given values and solving for A gives $A = 12.6^\circ$. Knowing angles A and B, we can find angle C since the sum of angles in a triangle is $180^\circ$, so $C = 180^\circ - A - B = 63.1^\circ$. Finally, using the Law of Sines again, we can find side c. The calculations match option A.

Find the Missing Parts of the Triangle B=104.3∘a=298 cm b=1324 cm\begin{array} { l } \mathrm { B } = 104.3 ^ { \circ } \\\mathrm { a } = 298 \mathrm {~cm} \\\mathrm {~b} = 1324 \mathrm {~cm}\end{array}B=104.3∘a=298 cm b=1324 cm​

Find the Missing Parts of the Triangle $\begin{array} { l } \mathrm { B } = 104.3 ^ { \circ } \\\mathrm { a } = 298 \mathrm {~cm} \\\mathrm {~b} = 1324 \mathrm {~cm}\end{array}$