# If sides A and B of a triangle have lengths of 8 and 3 respectively, and the angle between them is (5pi)/8, then what is the area of the triangle?

Oct 2, 2016

$11.09$

#### Explanation:

$\text{Let's consider the diagram}$

$\text{I have mentioned}$ $\frac{5 \pi}{8}$ $\text{as}$ ${112.5}^{\circ}$

$\text{We can find the area of a triangle given the length of two sides}$
$\text{and the angle between them using this formula}$

color(blue)(color(blue)("Area"color(blue)(=1/2*"color(blue)("A"color(blue)(*color(blue)("B""color(blue)(*sin(c)

$\rightarrow \frac{1}{2} \cdot 8 \cdot 3 \cdot \sin \left(112.5\right)$

$\rightarrow \frac{1}{\cancel{2}} ^ 1 \cdot {\cancel{24}}^{12} \cdot \sin \left(112.5\right)$

$\rightarrow 12 \cdot \sin \left(112.5\right)$

$\rightarrow 12 \cdot 0.92$

color(green)(rArr11.09