In a right-angled triangle ABC, angle C is straight, leg BC = 6cm, angle A = 60 degrees. Find:

| March 15, 2021 | education

In a right-angled triangle ABC, angle C is straight, leg BC = 6cm, angle A = 60 degrees. Find: a) The remaining sides of the ABC triangle, b) the area of the ABC triangle, c) The length of the height drawn from the vertex C

The sum of the acute angles of the triangle is 90, then the angle ABC = (90 – BAC) = (90 – 60) = 30.

The leg AC lies against an angle of 30, then AC = AB / 2.

Let the length AC = X cm, then AB = 2 * X cm.

By the Pythagorean theorem, CB ^ 2 = AB ^ 2 – AC ^ 2.

36 = 4 * X ^ 2 – X ^ 2.

3 * X ^ 2 = 36.

X ^ 2 = 12.

X = AC = 2 * √3 cm.

AB = 2 * 2 * √3 = 4 * √3 cm.

The area of the triangle ABC is equal to: Sавс = ВС * АС / 2 = 6 * 2 * √3 / 2 = 6 * √3 cm2.

Also Savs = AB * CH / 2.

CH = 2 * Savs / AB = 2 * 6 * √3 / 4 * √3 = 3 cm.

Answer: AB = 4 * √3 cm, AC = 2 * √3 cm, CH = 3 cm.



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