Trigonometry

Given triangle ABC with a = 16, b = 14, and Beta = 54°, find the value of c.
A. 3.1 and 20
B. 4.1 and 15
C. 15
D. 3.1

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  1. Use Law of Cosines:

    cosB = (a^2+c^2-b^2)/2ac.
    0.58779 = (256+c^2-196)/32c
    0.58779 = (c^2+60)/32c
    Cross multiply:
    18.81c = c^2+60
    c^2-18.81c+60 = 0.
    c = 4.1,and 14.7. Use Quadratic Formula.

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