ambiguous sine law (side,side,angle)

Question

suppose u know angle a, and side a and side b, depending upon the lengths of side a and b, there are different solutions.

give examples to illustrate. 

 

 

Answer 1

if you are given 2 angles and 1 side, it is not ambiguous because given 2 angles you actually know the third angle also because the three angles sum to 180 degrees. So the three angles establish a series of similar triangles, and the 1 side defines exactly which one.

 

However with 2 sides and 1 angle, the angle between the sides can be either acute or obtuse because the sine of an angle in the second quadrant and the sine of its reference angle (first quadrant) have the same value. Remember, sine is positive in quadrants I and II.