# Given a right-angled triangle ABC, an angle C of a straight line. It is known that AC = 20, BC = 10. Find cos B.

March 24, 2021 | education

| 1. By the Pythagorean theorem, it is known that the hypotenuse of a triangle is equal to the square root of the sum of the squares of the legs.

2. Let’s calculate the hypotenuse ab of the triangle abc, if it is known that the leg bc is 10 centimeters, and the leg ac is 20 centimeters.

ab = (bc ^ 2 + ac ^ 2) 1/2 = (10 ^ 2 + 20 ^ 2) 1/2 = 500 ^ 1/2 = 22.36 centimeters.

3. The cosine of an acute angle of a right-angled triangle is the ratio of the adjacent leg to the hypotenuse.

Find the cosine of the angle B.

cosB = bc: ab = 10: 22.36 = 0.45.

Answer: СsB is equal to 0.45.

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