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?

1 Answer
Mar 7, 2016

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 #pi//8# where we know that the length of A is 3 units.

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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 #pi//24#. In fact we know that the angles in a triangle add up to #pi# so the unknown angle must be:

#theta = pi-pi/8 - pi/24 = (5pi)/6#

Attempting to complete the triangle using a side of 6 units at the prescribed angles:

enter image source here

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.