Determine the number of possible solutions for a triangle with A = 30 a=20 and b=16

The answer is: Two possible solutions which are (0.53, 37.19)

Explanation:

Given:

A = 30°

a = 20

b = 16

Now use the law of Cosines:

a² = b² + c² - 2bc*cos (A)

Plug in the values:

20² = 16² + c² - (2 * (16) * c*cos (30))

400 = 256 + c² - 32c (0.866)

400 = 256 + c² - 27.71c

c² - 27.71c = 400 - 256

c² - 27.71c = 144

c² - 27.71c + 191.96 = 144 + 191.96

(c - 18.86) ² = 335.96

c - 18.86 = √336.95

c - 18.86 = ± 18.33

c = 18.86 ± 18.33

If c = 18.86 + 18.33, then c = 37.19

If c = 18.86 - 18.33, then c = 0.53

c = (0.53, 37.19) Two solutions!