In Triangle XYZ, what is the cosine ratio of <X? (Hint: Find the length of XY) The Numbers In The Triangle Are 7.5 & 6

To find the cosine ratio of angle X in Triangle XYZ, we first need to find the length of side XY.

In a right triangle, the cosine ratio is defined as the length of the adjacent side divided by the length of the hypotenuse. Let's label the sides of Triangle XYZ:

XZ (hypotenuse) = 7.5
XY (adjacent side) = ?
YZ (opposite side) = 6

Now, let's use the Pythagorean theorem to find the length of side XY:

XY^2 = XZ^2 - YZ^2
XY^2 = 7.5^2 - 6^2
XY^2 = 56.25 - 36
XY^2 = 20.25
XY = √20.25
XY = 4.5

Now that we know the length of side XY is 4.5, we can determine the cosine ratio of angle X:

cos(X) = adjacent/hypotenuse
cos(X) = XY/XZ
cos(X) = 4.5/7.5
cos(X) = 0.6

Therefore, the cosine ratio of angle X in Triangle XYZ is 0.6.

To find the cosine ratio of ∠X in Triangle XYZ, we need to determine the length of XY first.

Using the given numbers, we can use the Pythagorean theorem to find the length of XY. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

So, let's calculate the length of XY:

XY^2 = XZ^2 + YZ^2
XY^2 = 7.5^2 + 6^2
XY^2 = 56.25 + 36
XY^2 = 92.25

Taking the square root of both sides, we find:

XY = √92.25
XY ≈ 9.61 (rounded to two decimal places)

Now that we have the length of XY, we can proceed to find the cosine ratio of ∠X.

The cosine ratio relates the length of the adjacent side to the hypotenuse in a right triangle. In this case, XY is the adjacent side to ∠X, and XZ is the hypotenuse.

Therefore, the cosine ratio of ∠X is:

cos(∠X) = adj/hyp
cos(∠X) = XY/XZ
cos(∠X) = 9.61/7.5
cos(∠X) ≈ 1.28

So, the approximate cosine ratio of ∠X in Triangle XYZ is 1.28.