Determine the number of triangles ABC possible with the given part
C=58°
c=50
b=61
To determine the number of possible triangles ABC with the given parts, we need to check if the Law of Sines can be applied to form a unique triangle.
First, we need to find angle A using the Law of Sines:
sin(A)/a = sin(B)/b = sin(C)/c
sin(A)/a = sin(180-58-50)/61 = sin(72)/61
sin(A) = (61)(sin(72))/a
sin(A) = 0.08
A = sin^(-1)(0.08) ≈ 4.5°
Now, we need to determine how many possible triangles can be formed:
Case 1: A = 4.5° and B = 180-58-4.5 ≈ 117.5°
For this case, the triangle can be formed because the sum of angles A and B is less than 180°.
Therefore, a triangle ABC is possible with the given parts.