Question

what is \\(\sin(b)\\)?

\\(\sin(b) = \frac{?}{\quad}\\)

hint: remember sohcahtoa.

Explanation:

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<reasoning>

Identify the sides of the right triangle relative to angle B

\[

$$\begin{aligned} &\text{Opposite side} = 6\\ &\text{Adjacent side} = \sqrt{13}\\ &\text{Hypotenuse} = 7 \end{aligned}$$

\]

Apply the sine ratio formula

\[
\sin(B) = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{6}{7}
\]
</reasoning>

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

\(\sin(B) =\) <blank>\(\frac{6}{7}\)</blank>
</answer>

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"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Geometry",
"Right Triangle Trigonometry"
]
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Answer:

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</pre_analysis>

<reasoning>

Identify the sides of the right triangle relative to angle B

\[

$$\begin{aligned} &\text{Opposite side} = 6\\ &\text{Adjacent side} = \sqrt{13}\\ &\text{Hypotenuse} = 7 \end{aligned}$$

\]

Apply the sine ratio formula

\[
\sin(B) = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{6}{7}
\]
</reasoning>

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

\(\sin(B) =\) <blank>\(\frac{6}{7}\)</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Geometry",
"Right Triangle Trigonometry"
]
}
</post_analysis>