State whether the given measurements determine zero, one, or two triangles. B = 86°, b = 21, c = 18?

Method 1 : By drawing
Draw the triangle(s) by using the given data.
In this case, only 1 triangle is drawn.


Method 2 : Using sine law
Use sine law to find angle C.
Since sine function is position when the angle is in the 1st quadrant or the 2nd,
then C = θ (where 0° < θ < 90°) or C = 180° - θ (where 90° < θ < 180°)
If C = 180° - θ is rejected due to B + C > 180°, there is only 1 triangle.
Otherwise, there are 2 triangles.

In this case :
b/sinB = c/sinC (sine law)
21/sin86° = 18/sinC
sinC = sin86° × (18/21)
C = 58.8° or C = 180° - 58.8°
C = 58.8° or C = 121.2° (rejected for B + C = 207.2° > 180°)

Since there is only 1 possible value of angle C, there is only 1 triangle.