SOLUTION: Angle A in a triangle is 35°, side a is 9 cm, and side b is 12 cm. Find both possible values for side c.

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Question 1196605: Angle A in a triangle is 35°, side a is 9 cm, and side b is 12 cm. Find both possible values for side c.
Found 3 solutions by MathLover1, ikleyn, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


From the angle A, side b, and side a, we calculate side+c by using the Law of Cosines and quadratic equation:

a%5E2+=b%5E2%2Bc%5E2+-2bc%2Acos%28A%29
9%5E2+=12%5E2%2Bc%5E2+-2%2A12c%2Acos%2835%29
81+=144%2Bc%5E2+-24c%2A0.819152
0+=144-81%2Bc%5E2+-19.6596%2Ac+
c%5E2+-19.6596%2Ac+%2B63=0

c+=+%28-%28-19.6596%29+%2B-+sqrt%28+%28-19.6596%29%5E2-4%2A1%2A63+%29%29%2F%282%2A1%29+

c+=+%2819.6596+%2B-+sqrt%28+386.49987216-252+%29%29%2F2+
c+=+%2819.6596+%2B-+sqrt%28+134.49987216+%29%29%2F2+

c+=+%2819.6596+%2B-+11.597407993168128%29%2F2+

solutions:
c+=+%2819.6596+%2B11.597407993168128%29%2F2+=15.629
or
c+=+%2819.6596+-+11.597407993168128%29%2F2+=4.031
%28c+-+15.6285%29+%28c+-+4.0311%29+=+0
so, both possible values for side c are:
c+=15.629
c+=+4.031


Answer by ikleyn(52908) About Me  (Show Source):
Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
Angle A in a triangle is 35°, side a is 9 cm, and side b is 12 cm. Find both possible values for side c.
							
 sin (B) = 0.764768582
      , or ∡B = 130o (180o - 50o)
		
    If ∡B = 50o, ∡A = 35o (given), then ∡C = 95o      If ∡B = 130o, ∡A = 35o (given), then ∡C = 15o