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.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.