Applying the Laws of Sines or Cosines

Apr 2013
8
0
United States
Solve the triangle.

A = 19°, C = 102°, c = 6

choices are

B = 31°, a ≈ 18, b ≈ 15.8
B = 59°, a ≈ 2, b ≈ 5.3
B = 59°, a ≈ 18, b ≈ 15.8
B = 59°, a ≈ 18, b ≈ 5.3
 
Nov 2012
197
30
Normal, IL USA
The problem as stated can be solved without using the laws of sines or cosines, if I'm right that capital letters stand for angle measures and lower-case letters stand for lengths of sides, and c (for example) is the side opposite C. That would be a common convention.

19+102= 121 and 180-121=59. This eliminates your first choice.

The longest side will be opposite your largest angle. Since C is the largest angle, c=6 is the longest side. That eliminates the third and fourth choices, leaving only the second.

You could check out the second choice using the sine law if you want.