Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-$$\begin{array} { l }
\mathrm { b } = 15.5 \mathrm { ft } \
\mathrm { A } = 36 ^ { \circ } 10 ^ { \prime } \
\mathrm { C } = 95 ^ { \circ } 50 ^ { \prime }
\end{array}$$
A) $189.8 \mathrm { ft } ^ { 2 }$
B) $194.8 \mathrm { ft } ^ { 2 }$
C) $94.9 \mathrm { ft } ^ { 2 }$
D) $89.9 \mathrm { ft } ^ { 2 }$

Question

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-$$\begin{array} { l } 
\mathrm { b } = 15.5 \mathrm { ft } \
\mathrm { A } = 36 ^ { \circ } 10 ^ { \prime } \
\mathrm { C } = 95 ^ { \circ } 50 ^ { \prime }
\end{array}$$
A) $189.8 \mathrm { ft } ^ { 2 }$
B) $194.8 \mathrm { ft } ^ { 2 }$
C) $94.9 \mathrm { ft } ^ { 2 }$
D) $89.9 \mathrm { ft } ^ { 2 }$

Quizplus · Accepted Answer

First, find angle B using the fact that the sum of angles in a triangle is 180 degrees. Angle B = 180° - 36°10' - 95°50' = 48°. Then, use the formula for the area of a triangle when two angles and the included side are known: $Area = \frac{1}{2}b^2 \frac{\sin A \sin C}{\sin B}$. Substituting the given values and converting angles to radians for calculation, we get approximately $94.9 \, \text{ft}^2$.

Find the Area of Triangle ABC with the Given Parts