Michael B. answered • 11/13/12

I can provide your 'A-HA' moment

Maria,

as you say, there is not one unique solution for this triangle. Using Law of Sines, we get:

sin C = 18 * sin(50) / 14 = 0.98491

There are two angles which satisfy this constraint: C = 80.035 and C = 180 - 80.035 = 99.965

From these two answers we can derive the rest of the triangle by summing the angles to 180 degrees and then using Law of Sines to solve for the remaining side:

A = 49.965

B = 50

C = 80.035

a = 13.993

b = 14

c = 18

or

A = 30.035

B = 50

C = 99.965

a = 9.148

b = 14

c = 18

Michael B.

To be clear, it isn't

alwaysthe case that SSA produces two distinct solutions - there may be two, one, or zero. The case of one distinct solution necessarily turns out to be a right triangle.11/13/12