# If sides A and B of a triangle have lengths of 7 and 4 respectively, and the angle between them is (3pi)/4, then what is the area of the triangle?

Apr 7, 2018

:. color(orange)("Area of " Delta A_t =color(brown)(9.9 " sq units"

#### Explanation:

$a = 7 , b = 4 , \hat{C} = \frac{3 \pi}{4}$

Now we know the measure of two sides and the included angle.

$\therefore \text{Area of } \Delta {A}_{t} = \left(\frac{1}{2}\right) a b \sin C$

A_t = (1/2) * 7 * 4 * sin ((3pi)/4) = color(brown)(9.9 " sq units"