Final answer:
The given measurements determine one triangle.
Step-by-step explanation:
To determine whether the given measurements determine zero, one, or two triangles, we can use the Law of Sines. The Law of Sines states that in a triangle, the ratio of the length of a side to the sine of its opposite angle is constant. In this case, we have A = 35º, a = 6, and b = 13. We can use the Law of Sines to find the value of angle B:
sin(B) = (b * sin(A)) / a
sin(B) = (13 * sin(35º)) / 6
sin(B) ≈ 0.798
B ≈ 53.1º
Now, we can check if there is a valid triangle:
1. If A + B + C = 180º, where C is the remaining angle, then we have one triangle.
2. If A + B + C > 180º, then we have two triangles.
3. If A + B + C < 180º, then we have zero triangles.
Using the given measurements, we can calculate:
A + B + C = 35º + 53.1º + C = 88.1º + C
Since we know that the sum of angles in a triangle is 180º, we have 88.1º + C = 180º.
C = 180º - 88.1º = 91.9º
Therefore, A + B + C = 35º + 53.1º + 91.9º = 180º.
This means that the given measurements determine one triangle.