In a triangle ABC, AB = 8 cm, AC = 5 cm, angle A: angle B: angle C = 3: 4: 11 Find the area of the triangle.

1. Let’s make an equation.
Let one part be x cm, then, we write the equation as follows:
3 * x + 4 * x + 11 * x = 180;
Let’s count:
18 * x = 180;
x = 10 – one part;
We get:
angle A = 30 degrees;
angle B = 40 degrees;
angle C = 110 degrees.
2. It is necessary to lower the CH height. Then we get a new triangle АСН, which needs to be considered. In it, one angle is equal to 30 degrees, then we find СН:
CH = 0.5 * AC;
CH = 4 (cm).
3. Find S of the triangle:
S = 0.5 * 4 * 5;
S = 10 (cm2).
Answer: S = 10 (cm2).