In triangle ABC, angle C = 90 degrees, sin A = 13/14 AC = 6√3, find AB =?
| September 26, 2021 | education
1. It is known that sin2 A + cos2 A = 1. (Properties of sin i cos).
Then, cos A = √ (1 – sin2A) = √ 1 – (13/14) 2 = √ 1- (169/196) = √ 27/196 = 3√3 / 14.
2. Tg A = sin A: cos A. Tg A = CB: AC (properties of a right triangle).
Sin A: cos A = CB: AC.
CB = AC x sin A: cos A = (6√3 x 13 x 14): (14 x 3√3) = 2 x 13 = 26.
3. Behind the Pythagorean theorem AB ^ 2 = AC ^ 2 + CB ^ 2.
AB ^ 2 = 26 ^ 2 + (6√3) ^ 2 = 676 + 36 x 3 = 784.
AB = √784 = 28.
Answer: side AB is 28.
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