Question

Triangle X Y Z is a right triangle with right angle located at vertex Y.

X Y equals 8, Y Z equals 6, and X Z equals 10.

Which ratio describes cos left parenthesis X right parenthesis?

Answer 1

In a right triangle XYZ, where XY = 8, YZ = 6, and XZ = 10, the cosine of angle X is expressed as 3/5, making option (b) the correct ratio.

In a right-angled triangle XYZ, the cosine of angle X is defined as the adjacent side (in this case, YZ) divided by the hypotenuse (XZ). The given values are XY = 8, YZ = 6, and XZ = 10.

`\[ \cos(X) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = (YZ)/(XZ) = (6)/(10) = (3)/(5) \]`

So, the correct ratio that describes
`\(\cos(X)\)` is 3/5. Therefore, the answer is option (b) 3/5.

This ratio represents the cosine of angle X in the right triangle XYZ, reflecting the relationship between the adjacent side (YZ) and the hypotenuse (XZ).

The probable question may be:

Triangle X Y Z is a right triangle with right angle located at vertex Y.

X Y equals 8, Y Z equals 6, and X Z equals 10.

Which ratio describes cos left parenthesis X right parenthesis?

a. 3/4 b. 3/5 c. 4/3 d. 4/5