# A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 6, respectively. The angle between A and C is (pi)/4 and the angle between B and C is  pi/4. What is the area of the triangle?

Apr 8, 2018

color(maroon)("Measures of the given triangle are not consistent."

#### Explanation:

Angles Opposite to Equal Sides of a Triangle are Equal. Theorem: Angles opposite to equal sides of an isosceles triangle are equal.

Conversely, equal angles will have equal sides opposite to them.

Since $\hat{A} = \hat{B} = \frac{\pi}{4} , \text{ sides a & b must be equal.}$

But side a = 2, side b = 6.

Hence the measures of the given triangle are not consistent.