Answer:
no triangle at all
Explanation:
When two sides and an angle (SSA) of a triangle are given, we can use the Law of Cosines to determine whether the given measurements produce one triangle, two triangles, or no triangle at all.
The Law of Cosines states that in any triangle ABC, c² = a² + b² - 2ab cos(C), where a, b, and c are the lengths of the sides of the triangle and A, B, and C are the measures of the angles opposite those sides.
Given a = 17, c = 18.3, and A = 56°, we can use the Law of Cosines to find the value of b²:
b² = c² - a² + 2ab cos(A)
If the value of b² is positive, then the given measurements produce one triangle. If the value of b² is zero, then the given measurements produce one degenerate triangle. If the value of b² is negative, then the given measurements do not produce any triangle.
Calculating b² = 18.3² - 17² + 2(17)(18.3)cos(56°) = 0.3
As the value of b² is zero, the given measurements produce one degenerate triangle. A degenerate triangle is a triangle whose sides do not form a valid triangle, i.e the three sides are collinear.
Since, the value of b² is zero, it means that the three sides of the triangle are collinear and it will not form a triangle. The measurements provided do not produce any triangle.