Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as
-$$\begin{array} { l }
a = 28 \mathrm { ft } \
\mathrm { b } = 38 \mathrm { ft } \
\mathrm { c } = 42 \mathrm { ft }
\end{array}$$
A) No triangle satisfies the given conditions.
B) $\mathrm { A } = 40.6 ^ { \circ } , \mathrm { B } = 31 ^ { \circ } , \mathrm { C } = 108.4 ^ { \circ }$
C) $\mathrm { A } = 62 ^ { \circ } , \mathrm { B } = 40.6 ^ { \circ } , \mathrm { C } = 77.4 ^ { \circ }$
D) $\mathrm { A } = 40.6 ^ { \circ } , \mathrm { B } = 62 ^ { \circ } , \mathrm { C } = 77.4 ^ { \circ }$

Question

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as
-$$\begin{array} { l } 
a = 28 \mathrm { ft } \
\mathrm { b } = 38 \mathrm { ft } \
\mathrm { c } = 42 \mathrm { ft }
\end{array}$$
A) No triangle satisfies the given conditions.
B) $\mathrm { A } = 40.6 ^ { \circ } , \mathrm { B } = 31 ^ { \circ } , \mathrm { C } = 108.4 ^ { \circ }$
C) $\mathrm { A } = 62 ^ { \circ } , \mathrm { B } = 40.6 ^ { \circ } , \mathrm { C } = 77.4 ^ { \circ }$
D) $\mathrm { A } = 40.6 ^ { \circ } , \mathrm { B } = 62 ^ { \circ } , \mathrm { C } = 77.4 ^ { \circ }$

Quizplus · Accepted Answer

Using the law of cosines, we find angle A first: $ \cos A = \frac{b^2 + c^2 - a^2}{2bc} $. Calculating gives $ A \approx 40.6^\circ $. Then, using the law of sines, we find angle B: $ \sin B = \frac{b \sin A}{a} $, which gives $ B \approx 62^\circ $. Finally, angle C is found by subtracting the sum of angles A and B from 180°, giving $ C \approx 77.4^\circ $.

Find the Missing Parts of the Triangle a=28ftb=38ftc=42ft\begin{array} { l } a = 28 \mathrm { ft } \\\mathrm { b } = 38 \mathrm { ft } \\\mathrm { c } = 42 \mathrm { ft }\end{array}a=28ftb=38ftc=42ft​

Find the Missing Parts of the Triangle $\begin{array} { l } a = 28 \mathrm { ft } \\\mathrm { b } = 38 \mathrm { ft } \\\mathrm { c } = 42 \mathrm { ft }\end{array}$