Question

what is \\(\cos(b)\\)?

\\(\cos(b) = \frac{?}{}\\)

hint: remember sohcahtoa.

Explanation:

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<reasoning>

Identify the sides of the right triangle relative to angle B

\[

$$\begin{aligned} &\text{Adjacent side to } B = 12\\ &\text{Opposite side to } B = 5\\ &\text{Hypotenuse} = 13 \end{aligned}$$

\]

Apply the cosine ratio formula

\[
\cos(B) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{12}{13}
\]
</reasoning>

<answer>
What is \(\cos(B)\)?

\(\cos(B) =\) <blank>\(\frac{12}{13}\)</blank>
</answer>

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"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
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"Trigonometric Ratios"
]
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Answer:

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</pre_analysis>

<reasoning>

Identify the sides of the right triangle relative to angle B

\[

$$\begin{aligned} &\text{Adjacent side to } B = 12\\ &\text{Opposite side to } B = 5\\ &\text{Hypotenuse} = 13 \end{aligned}$$

\]

Apply the cosine ratio formula

\[
\cos(B) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{12}{13}
\]
</reasoning>

<answer>
What is \(\cos(B)\)?

\(\cos(B) =\) <blank>\(\frac{12}{13}\)</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Geometry",
"Trigonometric Ratios"
]
}
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