In ∆ABC, where ∠A= 20°, a = 2 cm, and b = 5 cm

Question

Determine the number of triangles that could be drawn with the given measures. Then, find the measures of the other angles and the other side in each possible triangle. Round to the nearest tenth, if necessary.

Answer 1

Sin B/b=Sin A/a →Sin 20/2 = Sin B/5 →Sin B=0.855 → Possible Bs: B=58.765º and B'=121.235º

Thus, Possible Cs are C=180-58.765-20=101.235º and C'=180-20-121.235=38.765º

Then possible cs are: Sin A/a= Sin C/c →Sin 20/2= Sin 101.235/c →c=5.736 cm

Sin 20/2 = Sin 38.765/c' → c'=3.661 cm