In a right-angled triangle, the height of the gon ABC (angle B = 90 °) of the leg AB = 5 and BC = 6. find cos C.

In a given right-angled triangle ABC legs AB = 5 and BC = 6, then the hypotenuse AC, opposite to the right angle B, can be calculated by the Pythagorean theorem, according to which the sides of a right-angled triangle are connected by the formula:

AC ^ 2 = AB ^ 2 + BC ^ 2,

AC ^ 2 = 5 ^ 2 + 6 ^ 2,

AC ^ 2 = 25 + 36,

AC ^ 2 = 61,

whence AC = 61 ^ 0.5.

Since, by definition, the cosine of an angle in a right-angled triangle is equal to the ratio of the adjacent leg to the hypotenuse, then

cos C = ВС / АС,

cos C = 6/61 ^ 0.5.

Answer: cos C = 6/61 ^ 0.5.