Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-$$\begin{array} { l }
\mathrm { A } = 21.3 ^ { \circ } \
\mathrm { b } = 12.2 \mathrm { in } . \
\mathrm { c } = 5.3 \mathrm { in }
\end{array}$$
A) $32.1$ in. 2
B) $9.7$ in.2
C) $30.1$ in. 2
D) $11.7$ in. 2

Question

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-$$\begin{array} { l } 
\mathrm { A } = 21.3 ^ { \circ } \
\mathrm { b } = 12.2 \mathrm { in } . \
\mathrm { c } = 5.3 \mathrm { in }
\end{array}$$
A) $32.1$ in. 2
B) $9.7$ in.2
C) $30.1$ in. 2
D) $11.7$ in. 2

Quizplus · Accepted Answer

To find the area of a triangle given two sides and an included angle, you can use the formula: $$ \text{Area} = \frac{1}{2}bc\sin(A) $$ where $b$ and $c$ are the lengths of two sides, and $A$ is the included angle. Plugging in the given values: $$ \text{Area} = \frac{1}{2} \times 12.2 \times 5.3 \times \sin(21.3^\circ) $$ Using a calculator: $$ \text{Area} \approx \frac{1}{2} \times 12.2 \times 5.3 \times 0.361 $$ $$ \text{Area} \approx 11.7 \, \text{in}^2 $$ Therefore, the area of the triangle is approximately $11.7$ square inches.

Find the Area of Triangle ABC with the Given Parts A=21.3∘b=12.2in.c=5.3in\begin{array} { l } \mathrm { A } = 21.3 ^ { \circ } \\\mathrm { b } = 12.2 \mathrm { in } . \\\mathrm { c } = 5.3 \mathrm { in }\end{array}A=21.3∘b=12.2in.c=5.3in​

Find the Area of Triangle ABC with the Given Parts $\begin{array} { l } \mathrm { A } = 21.3 ^ { \circ } \\\mathrm { b } = 12.2 \mathrm { in } . \\\mathrm { c } = 5.3 \mathrm { in }\end{array}$