A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 5, respectively. The angle between A and C is #(5pi)/24# and the angle between B and C is # (pi)/24#. What is the area of the triangle?

1 Answer
Hriman
Mar 15, 2018

This triangle does not exist...

Explanation:

Just by looking at the angles, side A should correspond to the angle between side B and C, while side B should correspond to the angle between side A and C. Since side A is larger than side B but has a smaller angle corresponding to it, this triangle does not exist...

Proof with the Law of Sines:
#A= arcsin((SinB*a)/b)#
#A= arcsin((Sin((5pi)/24)*7)/5)= 1.02 rad#
#pi/24 rad ≠ 1.02 rad#

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