Question

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?

Answer 1

`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 = pi/4, " sides a & b must be equal."`

But side a = 2, side b = 6.

Hence the measures of the given triangle are not consistent.