# 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.

September 27, 2021 | education

| 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).

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