In a right-angled triangle ABC, angle C = 90, BC = 3 cm, cosine of angle B = 0.6. Find AB and AC

1. Leg BC is adjacent to the angle at apex C, AB is the hypotenuse. Based on the fact that

their ratio is the cosine of the angle, we calculate the length of the hypotenuse:

0.6 = BC / AB;

AB = BC / 0.6 = 3 / 0.6 = 5 centimeters.

2. We calculate the length of the leg AC, applying the Pythagorean theorem:

AC ^ 2 = AB ^ 2 – BC ^ 2 = 25 – 9 = 16;

AC = √16 = 4 centimeters.

Answer: the length of the AC leg is 4 centimeters, the length of the hypotenuse AB is 5 centimeters.




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