Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all.
b=4, c=5, B=40 degrees.

Question

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all.
b=4, c=5, B=40 degrees.

anonymous · Answer

Draw the angle (40 degrees) and measure one side to be five units (side c).  From the end of that side away from the angle, draw an arc of radius four.  How many points of intersection are there with the opposite side of the angle?

anonymous · Answer

I'm sorry but after drawing the triangle I'm still rather confused on how to find the points of intersection are at the opposite side.

anonymous · Answer

OK.  Drawing not to scale.|dw:1404949828842:dw|Swing side b around.  How many points does it hit the other side?

anonymous · Answer

Is this the point where I would use the Pythagorean theorem?

anonymous · Answer

No, the question is how many times does the segment on the left go exactly to the segment on the top?  If you think about it, There are two triangles that you can make with a forty degree angle, an adjacent side of five, and an opposite side of four.  Neither will be a right triangle, so the Pythagorean Theorem doesn't apply.