State whether the given measurements determine zero, one, or two triangles. B = 84°, b = 28, c = 25?

Solution:

B = 84°, b = 28, c = 25 [Given]

By applying sine law

sinB/b = sinC/c

Substituting the values

sin 84°/28 = sinC/25

By further calculation

sin C = (sin 84°×28)/ 25

So we get

C = 62.6188° or 117.4°

As B = 84°, C cannot be 117.4°

As the angle of a triangle does not exceed 180°, there is only one triangle.

Therefore, the given measurements determine one triangle.

State whether the given measurements determine zero, one, or two triangles. B = 84°, b = 28, c = 25?

Summary:

The given measurements determine one triangle. B = 84°, b = 28, c = 25.