# Triangle ABC rectangular angle C 90 degrees angle A 30 degrees find BC and AB if the sum of sides AB and BC is 18 cm.

July 28, 2021 | education

| The desired leg BC lies opposite the angle 30, therefore, its length is equal to half the length of the hypotenuse AB.

AB = 2 * BC. (1).

By condition, AB + BC = 18 cm. (2).

Let us solve the system of two equations 1 and 2 by the substitution method.

AB = 18 – BC.

18 – BC = 2 * BC.

3 * BC = 18.

BC = 18/3 = 6 cm.

AB = 2 * BC = 2 * 6 = 12 cm.

Answer: The length of the side AB = 12 cm, the length of the side BC = 6 cm.

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