Determine the number of triangles ABC possible with the given parts.
b=20
A=50
C=50
To determine the number of triangles possible with the given parts, we need to consider the side lengths of the triangle as well as the given angles.
Given:
b = 20
A = 50 degrees
C = 50 degrees
To find side length 'a' we can use the law of sines:
a / sinA = b / sinB
a / sin50 = 20 / sin80
a = 20 * sin50 / sin80
a ≈ 20 * 0.766 / 0.984
a ≈ 15.4
Now we have side lengths a = 15.4, b = 20, and angles A = 50 degrees, B = 30 degrees, C = 100.
We can see that the sum of angles A, B, and C is 130 degrees, which is greater than 180 degrees, so it is not possible to form a triangle with these given parts.
Therefore, no triangle is possible with the given parts.