Question

what is \\(\tan(b)\\)?
\\(\tan(b) = \frac{?}{}\\)
hint: remember sohcahtoa.

Explanation:

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<reasoning>

Identify the sides relative to angle B

\[

$$\begin{aligned} &\text{Opposite side} = 4 \\ &\text{Adjacent side} = 5 \\ &\text{Hypotenuse} = \sqrt{41} \end{aligned}$$

\]

Apply the tangent ratio formula

\[
\tan(B) = \frac{\text{Opposite}}{\text{Adjacent}}
\]

Calculate the final value

\[
\tan(B) = \frac{4}{5}
\]
</reasoning>

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

\(\tan(B) =\) <blank>\(\frac{4}{5}\)</blank>
</answer>

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

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"Right Triangle Trigonometry",
"Tangent Ratio"
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</pre_analysis>

<reasoning>

Identify the sides relative to angle B

\[

$$\begin{aligned} &\text{Opposite side} = 4 \\ &\text{Adjacent side} = 5 \\ &\text{Hypotenuse} = \sqrt{41} \end{aligned}$$

\]

Apply the tangent ratio formula

\[
\tan(B) = \frac{\text{Opposite}}{\text{Adjacent}}
\]

Calculate the final value

\[
\tan(B) = \frac{4}{5}
\]
</reasoning>

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

\(\tan(B) =\) <blank>\(\frac{4}{5}\)</blank>
</answer>

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