A triangle has sides A, B, and C. Sides A and B have lengths of 3 and 8, respectively. The angle between A and C is π12 and the angle between B and C is 5π6. What is the area of the triangle?

1 Answer
Alan P.
Dec 14, 2015

No such triangle is possible.

Explanation:

If the angle between B and C is 5π6 then it is an obtuse angle and the side opposite that angle must be longer than any other side of the triangle. Therefore A can not be less than B.

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Assuming the values for the lengths of A and B have been accidentally switched doesn't work either.

∠b (i.e. the angle between A and C) =π12
and
∠a (i.e. the angle between B and C) =5π6

⇒∠c (i.e. the angle between B and C) =π12
(since the interior angles of a triangle must add up to π)

⇒ C = B =3

But then we would have 2 sides of a triangle (B and C) whose length was less than the third side (A), which is clearly impossible.

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