Law of sines

Question

The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used.

C = 37°, a = 19, c = 8

Answer 1

Angle C = 37^o and sides a = 19 and c = 8.

Law of sines : a/sinA=c/sinC ⇒ sinA = (a*sinC)/c

sinA = (19*sin37^o)/8 = (19*0.6018)/8 = (19*0.6018)/8 = 1.4293.

sinA ≅ 1.4293 > 1

This contradicts the fact that |sinA| ≤ 1. So, no triangle can be formed having sides a = 19 and c = 8 and a angle of C = 37^o.