Question

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

$a=6,b=4,C=60°$

Short answer

Required area of the triangle is$10.39squareunits$

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 b\times \sin \left(C\right)$

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

Step 2. Calculation

$Fromtheabovefigure,theareaofthetriangleis:$

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

localid="1646744803732" $$\begin{gathered} Given, \\ a=6,b=4,C=60° \\ Area=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\times 6\times 4\times \sin \left(60°\right) \\ =12\times 0.866 \\ =10.392 \\ \approx 10.39squareunits \end{gathered}$$