Answered

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Which is the correct cosine ratio for an angle with an adjacent side of 12 units and a hypotenuse of 16 units?

A. [tex]\( 0.7500 \)[/tex]

B. [tex]\( \frac{12}{16} \)[/tex]

C. [tex]\( 1.3333 \)[/tex]

Sagot :

GinnyAnswer
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
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