Find the missing parts of the triangle.
-$$\begin{array} { l }
\mathrm { B } = 24.4 ^ { \circ } \
\mathrm { b } = 5.19 \
\mathrm { a } = 6.28
\end{array}$$
If necessary, round angles to the nearest tenth and side lengths to the nearest hundredth.
A) $\mathrm { A } _ { 1 } = 29.99 ^ { \circ } , \mathrm { C } _ { 1 } = 125.61 ^ { \circ } , \mathrm { c } 1 = 10.21$;
B) $\mathrm { A } = 29.99 ^ { \circ } , \mathrm { C } = 125.61 ^ { \circ } , \mathrm { c } = 10.21$
$\mathrm { A } _ { 2 } = 150.01 ^ { \circ } , \mathrm { C } _ { 2 } = 5.59 ^ { \circ } , \mathrm { c } _ { 2 } = 1.22$
C) no such triangle
D) $\mathrm { A } = 150.01 ^ { \circ } , \mathrm { C } = 5.59 ^ { \circ } , \mathrm { C } = 1.22$

Question

Find the missing parts of the triangle.
-$$\begin{array} { l } 
\mathrm { B } = 24.4 ^ { \circ } \
\mathrm { b } = 5.19 \
\mathrm { a } = 6.28
\end{array}$$
If necessary, round angles to the nearest tenth and side lengths to the nearest hundredth.
A) $\mathrm { A } _ { 1 } = 29.99 ^ { \circ } , \mathrm { C } _ { 1 } = 125.61 ^ { \circ } , \mathrm { c } 1 = 10.21$;
B) $\mathrm { A } = 29.99 ^ { \circ } , \mathrm { C } = 125.61 ^ { \circ } , \mathrm { c } = 10.21$
$\mathrm { A } _ { 2 } = 150.01 ^ { \circ } , \mathrm { C } _ { 2 } = 5.59 ^ { \circ } , \mathrm { c } _ { 2 } = 1.22$
C) no such triangle
D) $\mathrm { A } = 150.01 ^ { \circ } , \mathrm { C } = 5.59 ^ { \circ } , \mathrm { C } = 1.22$

Quizplus · Accepted Answer

The Law of Sines can be used to find the missing parts of the triangle.$$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$Using the given information, we can solve for the missing parts:$$\frac{6.28}{\sin A} = \frac{5.19}{\sin 24.4^\circ}$$$$\sin A = 0.4999$$$$A = 29.99^\circ$$$$\frac{6.28}{\sin A} = \frac{c}{\sin C}$$$$\frac{c}{\sin C} = 10.21$$$$C = 125.61^\circ$$$$c = 10.21$$

Find the Missing Parts of the Triangle B=24.4∘b=5.19a=6.28\begin{array} { l } \mathrm { B } = 24.4 ^ { \circ } \\\mathrm { b } = 5.19 \\\mathrm { a } = 6.28\end{array}B=24.4∘b=5.19a=6.28​

Find the Missing Parts of the Triangle $\begin{array} { l } \mathrm { B } = 24.4 ^ { \circ } \\\mathrm { b } = 5.19 \\\mathrm { a } = 6.28\end{array}$