Find the area of the triangle ABC if AB = 9cm, AC = 12cm, angle B = 100 degrees, angle C = 50 degrees.

Since the sum of all angles in a triangle is 180 degrees, knowing that angles B and C are equal to 100 and 50 degrees, respectively, we calculate the value of angle A:

1) 180 – (100 + 50) = 30 (degrees)

2) On two sides and the angle between them, you can find the area of a triangle using the formula:

S = ½ ab sin α, in our case the formula will look like this:

S = 1/2 * AB * AC * sinA. With AB = 9cm, AC = 12cm, sin 30 ° = 1/2, we find the area:

S = 1/2 * 9 * 12 * sin 30 ° = 1/2 * 9 * 12 * 1/2 = 27 (cm2).

Answer: the triangle has an area of 27 cm2.