In triangle ABC, angle B is 90 degrees, AC 17cm, BC 8cm. find cos C, and ctg A
To calculate cos C, we use the cosine theorem. The cosine of an acute angle of a right-angled triangle is the ratio of the adjacent leg to the hypotenuse:
cos C = CB / AC;
cos C = 8/17 ≈ 0.47.
The cotangent of an acute angle of a right-angled triangle is the ratio of the adjacent leg to the opposite one:
ctg A = AB / BC.
To do this, you need to find the length of the leg AB. We apply the Pythagorean theorem, according to which the square of the hypotenuse is equal to the sum of the squares of the quatets:
AC² = AB² + BC²;
AB² = AC² – BC²;
AB² = 172 – 82 = 289 – 64 = 225;
AB = √225 = 15 cm.
ctg A = 15/8 ≈ 1.88.
Answer: the cosine of the angle ∠С is equal to 0.47, which corresponds to 62º; the cotangent of the angle ∠A is 1.88, which corresponds to 28º.