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.

B = 137°, c = 9, b = 14

Answer 1

Draw ΔABC as shown in the figure below.
m∠B = 137°, b = 14, c = 9.

From the Law of Sines,
sin(C)/c = sin(B)/b
or
sin(C)/9 = sin(137°)/14
sin(C) = (9/14)*sin(137°) = 0.4384
m∠C = arcsin(0.4384) = 26°

Because the sum of angles in a triangle is 180°, therefore
m∠A = 180 -137 - 26 = 17°

From the Law of Sines,
a/sin(A) = b/sin(B)
or
a/sin(17°) = 14/sin(137°)
a = (sin(17°)/sin(127°))*14 = 6

Answer:
The solution for the triangle is
a = 6, b = 14, c = 9
m∠A = 17°, m∠B = 137°, m∠C = 26°