Question

What is the cosine ratio of ∠Z?

The triangle XZY is right angle triangle. Angle Y is right angle. The length of YZ is 12, the length of XY is 16, and the length of XZ is 20

Answer 1

The cosine ratio of angle Z in triangle XZY, with YZ = 12 and XZ = 20, is 0.6.

Step-by-step explanation:

The cosine ratio of an angle in a right triangle is defined as the length of the adjacent side divided by the length of the hypotenuse. In triangle XZY, with a right angle at Y and sides of length YZ = 12, XY = 16, and XZ = 20, we want to find the cosine ratio of ∠Z. Since ∠Y is the right angle, side YZ is adjacent to ∠Z, and side XZ is the hypotenuse.

Therefore, the cosine of ∠Z is calculated as:

cos(∠Z) = (length of adjacent side YZ) / (length of hypotenuse XZ)

cos(∠Z) = 12 / 20

cos(∠Z) = 0.6

The cosine ratio of angle Z in this right triangle is 0.6.

Answer 2

The cosine ratio of ∠Z in the right triangle XZY is 12 / 20.

How to find the cosine ratio?

To find the cosine ratio of angle ∠Z in right triangle XZY, you can use the cosine function, which is defined as:

cos(∠Z) = adjacent side / hypotenuse

In this case, the adjacent side is XZ, and the hypotenuse is XY.

cos(∠Z) = YZ / XZ

Given that the length of YZ is 12 and the length of XZ is 20 :

cos(∠Z) = 12 / 20

Now, simplify the fraction:

cos(∠Z) = 3 / 5

So, the cosine ratio of angle ∠Z is 3 / 5.