How many triangles exist that fit the following criteria?C=60°,c=7.5,b=5

To solve this problem, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

Given: C = 60° c = 7.5 b = 5

We can write the Law of Sines as:

b/sin(B) = c/sin(C)

Substituting the given values:

5/sin(B) = 7.5/sin(60°)

Solving for sin(B):

sin(B) = 5 * sin(60°) / 7.5

sin(B) = 0.57735

Now, we find the angle B:

B = arcsin(0.57735)

B = 35.26°

Now, we can find angle A using the fact that the sum of the angles in a triangle is 180°:

A = 180° - B - C

A = 180° - 35.26° - 60°

A = 84.74°

Since all the angles are less than 180°, there is only one triangle that fits the given criteria.