Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-$$\begin{array} { l }
\mathrm { A } = 31 ^ { \circ } 40 ^ { \prime } \
\mathrm { b } = 19.3 \mathrm {~m} \
\mathrm { c } = 7.9 \mathrm {~m}
\end{array}$$
A) $20 \mathrm {~m} ^ { 2 }$
B) $80 \mathrm {~m} ^ { 2 }$
C) $40 \mathrm {~m} ^ { 2 }$
D) $82 \mathrm {~m} ^ { 2 }$

Question

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-$$\begin{array} { l } 
\mathrm { A } = 31 ^ { \circ } 40 ^ { \prime } \
\mathrm { b } = 19.3 \mathrm {~m} \
\mathrm { c } = 7.9 \mathrm {~m}
\end{array}$$
A) $20 \mathrm {~m} ^ { 2 }$
B) $80 \mathrm {~m} ^ { 2 }$
C) $40 \mathrm {~m} ^ { 2 }$
D) $82 \mathrm {~m} ^ { 2 }$

Quizplus · Accepted Answer

The area of the triangle can be calculated using the formula: $ \text{Area} = \frac{1}{2}bc\sin(A) $. Convert angle A to decimal degrees: $31^\circ 40' = 31.6667^\circ$. Then, calculate: $ \text{Area} = \frac{1}{2} \times 19.3 \times 7.9 \times \sin(31.6667^\circ) \approx 40 \mathrm{~m}^2 $.

Find the Area of Triangle ABC with the Given Parts