Determine the number of triangles ABC possible with the given parts.
Given:
A= 50°
b= 20
C = 50°
To find the number of possible triangles ABC with the given parts, we first need to determine whether the side lengths given form a valid triangle.
We can use the law of sines to check if it forms a valid triangle. The law of sines states that in any triangle ABC, the ratio of the length of a side to the sine of the angle opposite that side is constant:
a/sin(A) = b/sin(B) = c/sin(C)
Given:
A = 50°
b = 20
C = 50°
We have:
a/sin(50°) = 20/sin(B)
We can solve for sin(B) by rearranging the equation:
sin(B) = 20 / (a/sin(50°))
sin(B) = (20*sin(50°))/a
Since angles of any triangle add up to 180°, we can find angle B by:
B = 180° - 50° - 50°
B = 80°
Now we can determine the length of side "a" using the law of sines:
a/sin(A) = b/sin(B)
a/sin(50°) = 20/sin(80°)
a = (20*sin(50°))/sin(80°)
a ≈ (20*0.766)/0.985
a ≈ 15.53
So, the side lengths form a valid triangle. Therefore, there can be only one possible triangle ABC with the given parts.