# A triangle has sides A, B, and C. Sides A and B have lengths of 4 and 7, respectively. The angle between A and C is (pi)/4 and the angle between B and C is  (2pi)/3. What is the area of the triangle?

Feb 28, 2016

area ≈ 3.623 square units

#### Explanation:

To find the area of this triangle given sides A and B , use

$\text{ area } = \frac{1}{2} A B \sin \theta$

where $\theta \text{ is the angle between A and B}$

The sum of the 3 angles in the triangle $= \pi$

$\Rightarrow \theta = \left[\pi - \left(\frac{\pi}{4} + \frac{2 \pi}{3}\right)\right] = \pi - \frac{11 \pi}{12} = \frac{\pi}{12}$

$\text{ area " = 1/2 xx4 xx 7 xx sin(pi/12) ≈ 3.623" square units }$