can a triangle not exist if A

Question

can a triangle not exist if A<90 and a<b sin A or if A>90 and a<b?

e.mccormick · Answer

In a standard diagram of the triangle, the three angles of a triangle, A+B+C = 180 degrees or pi radians. The side a is opposite angle A, b opposite B, and so on.  Now, with that defined, look at the range of the sine of A and what that means for the values of the trigonometric ratios. between the sides.

It might aso help if you tried looking at it in standard form on the unit circle.

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How must those things be related?  Take a few sine values of angles, look for treneds.