# A triangle has sides A, B, and C. Sides A and B have lengths of 8 and 2, respectively. The angle between A and C is pi/4 and the angle between B and C is  pi/3. What is the area of the triangle?

Jul 10, 2017

Area of triangle is $7.73$ sq.unit

#### Explanation:

Angle between sides $A \mathmr{and} C$ is $\angle b = \frac{\pi}{4} = \frac{180}{4} = {45}^{0}$
Angle between sides $B \mathmr{and} C$ is $\angle a = \frac{\pi}{3} = \frac{180}{3} = {60}^{0}$
Angle between sides $A \mathmr{and} B$ is $\angle c = 180 - \left(60 + 45\right) = {75}^{0}$

Now we know sides $A , B$ and their included angle $\angle c$

Sides $A = 8 , B = 2 , \angle c = {75}^{0}$

Area of triangle is ${A}_{t} = \frac{A \cdot B \cdot \sin c}{2} = \frac{8 \cdot \cancel{2} \cdot \sin 75}{\cancel{2}} = 8 \cdot \sin 75$ or

${A}_{t} \approx = 7.73 \left(2 \mathrm{dp}\right)$sq.unit

Area of triangle is $7.73 \left(2 \mathrm{dp}\right)$sq.unit [Ans]