A triangle has sides A, B, and C. Sides A and B have lengths of 3 and 6, respectively. The angle between A and C is #(pi)/8# and the angle between B and C is # (pi)/24#. What is the area of the triangle?
This triangle is not possible.
We begin by attempting to draw the triangle in question. Let's start with the vertex for the first angle that we were given. This is the angle between sides A and C which is
We know that side B has length 6 units - twice as long as side A. It becomes clear that to draw B, it must be at a large angle to A, which makes sense from the angle we got for the vertex between B and C which is a very small angle
Attempting to complete the triangle using a side of 6 units at the prescribed angles:
We come to realize that this is not a possible triangle - there is no way to make side B meet side C. Either one of the angles given is wrong or one of the lengths is wrong.