Answer to Question #98391 in Trigonometry for Maria Rafaella Magri

Question

State whether the given measurements determine zero, one, or two triangles.
C = 37°, a = 16, c = 14

Answer 1

C = 37 , a = 16 , c = 14

h = a * sin(C) = 16 * sin(37) = 9.629.

Necessary condition : h(=9.629) < c(=14) < a(=16), So the possible triangles are two.

sin(A) = (16) * [sin(37) / 14] = 0.6878.

A = sin ^-1(0.6878) = 43.46⁰.

These are the two angles , A1 = 43.46⁰ and A2 = 180 - 43.46⁰ = 136.54⁰

Triangle1, A1 =43.46⁰, B1 = 180-43.46-37=99.54⁰ and side b = [c/sin(C)] * sin(B) = [14/sin(37)] * sin(99.54) = 22.94 .

Triangle2, A2 = 136.54, B2 = 180-136.54-37=6.46⁰ and b = [c/sin(C)] * sin(B) = [14/sin(37)] * sin(6.46) = 2.61 .