# A triangle has sides A, B, and C. Sides A and B have lengths of 3 and 2, respectively. The angle between A and C is #(11pi)/24# and the angle between B and C is # (pi)/8#. What is the area of the triangle?

##### 1 Answer

If

#### Explanation:

The third angle opposite sides

As side

Hence area of triangle is

=

We have not used

or

and area of triangle is

**Why this dichotomy? The fact is that we need either (a) one side and both angles on it; or (b) two sides and included angle and (iii) three sides of a triangle to identify a triangle and find area or other sides and angles of a triangle. However here we have been given four parameters and they give two different results depending on whether we take side #A=3# or #B=2# into consideration. In short, given three angles (third is derivable from other two), the two sides are not compatible and in fact refer to two different triangles.**