Question

How do you determine the number of possible solutions using the rule of law of sines given a=13.7, A=25°26', B=78°?

Answer 1

Solve triangle knowing a = 13.7; A = 25.26; B = 78

Explanation:

Find C, b and c.
C = 180 - A - B = 180 - 25.26 - 78 = 76.74 deg
Use the Law of sines to find c -->

`c = a(sin C/sin A) = 13.7(0.97/0.43) = 30.90`

There are 2 possible answers because (0.97) is the sine value of another angle (180 - 76.74) = 103.26 deg. However, this solution is rejected because the total angle measures of a triangle must be 180 deg.
`b = 13.7(sin B/sin A) = 13.7(0.98/0.43) = 31.22`