Find the missing parts of the triangle.
-$$\begin{array} { l }
\mathrm { B } = 105.3 ^ { \circ } \
\mathrm { a } = 298 \mathrm {~cm} \
\mathrm {~b} = 1103 \mathrm {~cm}
\end{array}$$
If necessary, round angles the nearest tenth and side lengths to the nearest $\mathrm { cm }$.
A) $\mathrm { A } = 15.1 ^ { \circ } , \mathrm { C } = 59.6 ^ { \circ } , \mathrm { c } = 987 \mathrm {~cm}$
B) $\mathrm { A } = 18.1 ^ { \circ } , \mathrm { C } = 56.6 ^ { \circ } , \mathrm { c } = 987 \mathrm {~cm}$
C) no such triangle
D) $\mathrm { A } = 59.6 ^ { \circ } , \mathrm { C } = 15.1 ^ { \circ } , \mathrm { c } = 987 \mathrm {~cm}$

Question

Find the missing parts of the triangle.
-$$\begin{array} { l } 
\mathrm { B } = 105.3 ^ { \circ } \
\mathrm { a } = 298 \mathrm {~cm} \
\mathrm {~b} = 1103 \mathrm {~cm}
\end{array}$$
If necessary, round angles the nearest tenth and side lengths to the nearest $\mathrm { cm }$.
A) $\mathrm { A } = 15.1 ^ { \circ } , \mathrm { C } = 59.6 ^ { \circ } , \mathrm { c } = 987 \mathrm {~cm}$
B) $\mathrm { A } = 18.1 ^ { \circ } , \mathrm { C } = 56.6 ^ { \circ } , \mathrm { c } = 987 \mathrm {~cm}$
C) no such triangle
D) $\mathrm { A } = 59.6 ^ { \circ } , \mathrm { C } = 15.1 ^ { \circ } , \mathrm { c } = 987 \mathrm {~cm}$

Quizplus · Accepted Answer

Given $B = 105.3^\circ$ and sides $a = 298$ cm and $b = 1103$ cm, we can find the other angles using the Law of Sines: $\frac{a}{\sin A} = \frac{b}{\sin B}$. Since the sum of angles in a triangle is $180^\circ$, $A + B + C = 180^\circ$. With $B = 105.3^\circ$, we can calculate $A$ and $C$. The given solution correctly identifies $A = 15.1^\circ$ and $C = 59.6^\circ$ based on these principles, and side $c$ can be found using the Law of Sines again or by applying the Law of Cosines.

Find the Missing Parts of the Triangle B=105.3∘a=298 cm b=1103 cm\begin{array} { l } \mathrm { B } = 105.3 ^ { \circ } \\\mathrm { a } = 298 \mathrm {~cm} \\\mathrm {~b} = 1103 \mathrm {~cm}\end{array}B=105.3∘a=298 cm b=1103 cm​

Find the Missing Parts of the Triangle $\begin{array} { l } \mathrm { B } = 105.3 ^ { \circ } \\\mathrm { a } = 298 \mathrm {~cm} \\\mathrm {~b} = 1103 \mathrm {~cm}\end{array}$