# A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 12, respectively. The angle between A and C is (pi)/8 and the angle between B and C is  (3pi)/8. What is the area of the triangle?

##### 1 Answer
Aug 26, 2016

The Area of the $\Delta$=42sq. units.

#### Explanation:

We denote, by $\hat{A , B}$, the angle btwn. sides $A , \mathmr{and} , B$.

From Geometry, we know that, in any $\Delta$

$\hat{A , B} + \hat{B , C} + \hat{C , A} = \pi$

$\therefore \hat{A , B} + 3 \frac{\pi}{8} + \frac{\pi}{8} = \pi \Rightarrow \hat{A , B} = \frac{\pi}{2}$.

Thus, given $\Delta$ is a right-triangle, and, sides $A$ and $B ,$

having lengths $7$ and $12$ resp. are at right angle.

Accordingly, the Area of the $\Delta$=1/2712=42 sq. units.