To determine the correct cosine ratio for an angle with an adjacent side of 12 units and a hypotenuse of 16 units, follow these steps:
1. Understand the Cosine Ratio:
The cosine ratio in a right triangle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.
2. Identify the Values:
In this problem, the length of the adjacent side is 12 units and the length of the hypotenuse is 16 units.
3. Set Up the Cosine Ratio:
We use the definition of cosine:
[tex]\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\][/tex]
4. Substitute the Values:
Substituting the given values into the formula gives us:
[tex]\[
\cos(\theta) = \frac{12}{16}
\][/tex]
5. Simplify the Fraction:
Simplify the fraction to find the cosine ratio:
[tex]\[
\frac{12}{16} = 0.75
\][/tex]
So, the correct cosine ratio for the angle given the adjacent side of 12 units and hypotenuse of 16 units is [tex]\(0.75\)[/tex].
From the provided options, the correct answer is:
0.7500
