Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.
-$$\begin{array} { l }
a = 7.2 \mathrm { in } . \
\mathrm { b } = 13.7 \mathrm { in } . \
\mathrm { c } = 15.6 \mathrm { in } .
\end{array}$$
A) $\mathrm { A } = 29.5 ^ { \circ } , \mathrm { B } = 59.4 ^ { \circ } , \mathrm { C } = 91.1 ^ { \circ }$
B) No triangle satisfies the given conditions.
C) $\mathrm { A } = 25.5 ^ { \circ } , \mathrm { B } = 61.4 ^ { \circ } , \mathrm { C } = 93.1 ^ { \circ }$
D) $\mathrm { A } = 27.5 ^ { \circ } , \mathrm { B } = 61.4 ^ { \circ } , \mathrm { C } = 91.1 ^ { \circ }$

Question

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.
-$$\begin{array} { l } 
a = 7.2 \mathrm { in } . \
\mathrm { b } = 13.7 \mathrm { in } . \
\mathrm { c } = 15.6 \mathrm { in } .
\end{array}$$
A) $\mathrm { A } = 29.5 ^ { \circ } , \mathrm { B } = 59.4 ^ { \circ } , \mathrm { C } = 91.1 ^ { \circ }$
B) No triangle satisfies the given conditions.
C) $\mathrm { A } = 25.5 ^ { \circ } , \mathrm { B } = 61.4 ^ { \circ } , \mathrm { C } = 93.1 ^ { \circ }$
D) $\mathrm { A } = 27.5 ^ { \circ } , \mathrm { B } = 61.4 ^ { \circ } , \mathrm { C } = 91.1 ^ { \circ }$

Quizplus · Accepted Answer

To find the angles of the triangle, we can use the Law of Cosines. Given the sides $a$, $b$, and $c$, the angles opposite these sides can be found using the formula $\cos(A) = \frac{b^2 + c^2 - a^2}{2bc}$, and similarly for angles $B$ and $C$. Calculating these for the given side lengths and converting the cosine values to degrees will give the angles as in option D.

Find the Missing Parts of the Triangle a=7.2in.b=13.7in.c=15.6in.\begin{array} { l } a = 7.2 \mathrm { in } . \\\mathrm { b } = 13.7 \mathrm { in } . \\\mathrm { c } = 15.6 \mathrm { in } .\end{array}a=7.2in.b=13.7in.c=15.6in.​

Find the Missing Parts of the Triangle $\begin{array} { l } a = 7.2 \mathrm { in } . \\\mathrm { b } = 13.7 \mathrm { in } . \\\mathrm { c } = 15.6 \mathrm { in } .\end{array}$