Given ABC angles ABC are related as 1: 2: 3 BC 8cm find AB and AC.

univerkov | September 18, 2021 | education

Let the angle BAC = X0, then the angle ACB = 2 * X0, the angle ABC = 3 * X0.

The sum of the interior angles of a triangle is 180, then:

X + 2 * X + 3 * X = 180.

6 * X = 360.

X = 180/6 = 30.

Angle BAC = 30, angle ACB = 2 * 20 = 60, angle ABC = 3 * 30 = 90, therefore triangle ABC is rectangular.

The BC leg lies against an angle of 30, then AC = 2 * BC = 2 * 8 = 16 cm.

By the Pythagorean theorem, AB ^ 2 = AC ^ 2 – BC ^ 2 = 256 – 64 = 192.

AB = 8 * √3 cm.

Answer: Length AB = 8 * √3 cm, length AC = 16 cm.

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