Question

Given a triangle with a = 9, b = 11, A = 31°, what is (are) the possible length(s) of c? Round your answer to two decimal places.

A) 16.42 or 2.44
B) 6.61
C) 14.21
D) 16.42 or 3.41

Answer 1

You can use the Law of Cosines to figure this.
a² = b² +c² -2bc×cos(A)
c² -(2b×cos(A))c +b² -a² = 0
c² -18.8577c +40 = 0 . . . . . . . substituting the given values
Then we can use the quadratic formula to find c.
c = (18.8577 ±√(18.8577² -160))/2
c = (18.8577 ±13.9861)/2 ≈ {2.44, 16.42}

The appropriate choice is ...
A) 16.42 or 2.44