Given a right-angled triangle ABC, in which the angle C is straight, the leg BC is 6 cm and the angle A = 60. degrees.

| December 13, 2020 | education

Given a right-angled triangle ABC, in which the angle C is straight, the leg BC is 6 cm and the 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 dropped from the vertex C

Sin (CAB) = BC / AB => AB = BC / sin (CAB) = 6 / (√ (3) / 2) = 4 * √ (3). Since triangle ABC is rectangular and angle A = 60 °, then angle B = 30 °. By the property of the leg opposite to the angle of 30 °: AC = 0.5 * AB = 0.5 * 4 * √ (3) = 2 * √ (3). S = 1/2 * AC * BC = 1/2 * 6 * 2 * √ (3) = 6 * √ (3). Let us omit the CH height from the vertex of the right angle. Consider the ACH triangle: Sin (CAH) = CH / AC => CH = sin (CAH) * AC = √ (3) / 2 * 2 * √ (3) = 3.
Answer: AC = 2 * √ (3), AB = 4 * √ (3), S = 6 * √ (3), H = 3.



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