Question

In the given question find the area of the triangle. Round the answers to two decimal places.

$a=3,c=2,B=110°$

Short answer

Required area of the triangle is 2.82 square units.

Step-by-step solution

Step 1.

From the given triangle we can find the area of the triangle by the following formula:

$Area=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\times a\times c\times \sin \left(B\right)$

Step 2. Calculation

From the above figure, the area of the triangle is:

$$\begin{gathered} Area=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\times a\times c\times \sin \left(B\right) \\ Given, \\ a=3,c=2,B=110° \\ Area=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\times 3\times 2\times \times \sin \left(110°\right) \\ =3\times 0.9396 \\ =2.8188 \\ \approx 2.82squareunits \end{gathered}$$