Question

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

Answer 1

Answer:

1 Solution on edge

Step-by-step explanation:

Answer 2

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!