How do you figure out if there is a triangle, or no triangle?

I'm getting vex...

For example:

a=10, b=16.6, A=27 degree (produces two triangles).

Example 2:

a=18, b=25, A=70 degree (No Triangle).

Please explain, why.

Question

How do you figure out if there is a triangle, or no triangle?

I'm getting vex...

For example:

a=10, b=16.6, A=27 degree (produces two triangles).

Example 2:

a=18, b=25, A=70 degree  (No Triangle).

Please explain, why.

anonymous · Answer

I did notice that these two problems are quiet  different.

turingtest · Answer

I'm thinking that one way to see it is with the law of sines...

turingtest · Answer

$${a \over \sin A}={b \over \sin B}\to \sin B={b \over a} \sin A={25\over18}\sin(70)\approx1.3$$but trig functions can never be greater than one, so $$B=\sin^{-1}(1.3)$$is undefined, therefor no triangle.

turingtest · Answer

for the first triangle $$\sin B={16.6\over10}\sin(27)\approx0.75<1$$so angle B can be calculated, hence this obeys the law of sines and is a triangle.

anonymous · Answer

Thank you much.