Algebra-2

In a right triangle, the cosine (cos) of an angle is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.

In the given triangle, angle X is the angle for which we need to find the cosine value. The side adjacent to angle X is XY, which has a length of 6, and the opposite side is ZY, with a length of 8, and the hypotenuse is ZX.

Applying the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides, we have:



Given the information that XY = 6 and ZY = 8, we can now calculate the length of the hypotenuse ZX:

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