Find the missing parts of the triangle.
-$$\begin{array} { l }
\mathrm { A } = 96.1 ^ { \circ } \
\mathrm { b } = 15.2 \mathrm { ft } \
\mathrm { a } = 30.4 \mathrm { ft }
\end{array}$$
If necessary, round angles and side lengths to the nearest tenth.
A) no such triangle
B) $\mathrm { B } = 29.8 ^ { \circ } , \mathrm { C } = 54.1 ^ { \circ } , \mathrm { c } = 24.8 \mathrm { ft }$
C) $\mathrm { B } = 34.8 ^ { \circ } , \mathrm { C } = 49.1 ^ { \circ } , \mathrm { c } = 24.8 \mathrm { ft }$
D) $\mathrm { B } = 54.1 ^ { \circ } , \mathrm { C } = 29.8 ^ { \circ } , \mathrm { c } = 24.8 \mathrm { ft }$

Question

Find the missing parts of the triangle.
-$$\begin{array} { l } 
\mathrm { A } = 96.1 ^ { \circ } \
\mathrm { b } = 15.2 \mathrm { ft } \
\mathrm { a } = 30.4 \mathrm { ft }
\end{array}$$
If necessary, round angles and side lengths to the nearest tenth.
A) no such triangle
B) $\mathrm { B } = 29.8 ^ { \circ } , \mathrm { C } = 54.1 ^ { \circ } , \mathrm { c } = 24.8 \mathrm { ft }$
C) $\mathrm { B } = 34.8 ^ { \circ } , \mathrm { C } = 49.1 ^ { \circ } , \mathrm { c } = 24.8 \mathrm { ft }$
D) $\mathrm { B } = 54.1 ^ { \circ } , \mathrm { C } = 29.8 ^ { \circ } , \mathrm { c } = 24.8 \mathrm { ft }$

Quizplus · Accepted Answer

Given $A = 96.1^\circ$ and sides $a = 30.4 \, \text{ft}$ and $b = 15.2 \, \text{ft}$, we can use the Law of Sines to find angle B. Since $\frac{\sin A}{a} = \frac{\sin B}{b}$, solving for B gives $B \approx 29.8^\circ$. Knowing angles A and B, angle C can be found by subtracting their sum from 180°, giving $C \approx 180^\circ - 96.1^\circ - 29.8^\circ = 54.1^\circ$. Finally, using the Law of Sines again to find side c, we get a consistent solution with choice B.

Find the Missing Parts of the Triangle A=96.1∘b=15.2fta=30.4ft\begin{array} { l } \mathrm { A } = 96.1 ^ { \circ } \\\mathrm { b } = 15.2 \mathrm { ft } \\\mathrm { a } = 30.4 \mathrm { ft }\end{array}A=96.1∘b=15.2fta=30.4ft​

Find the Missing Parts of the Triangle $\begin{array} { l } \mathrm { A } = 96.1 ^ { \circ } \\\mathrm { b } = 15.2 \mathrm { ft } \\\mathrm { a } = 30.4 \mathrm { ft }\end{array}$