Question

what is \\(\tan(a)\\)?

\\(\tan(a) = \frac{?}{\quad}\\)

hint: remember sohcahtoa.

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Right Triangle Trigonometry",
"Tangent Ratio"
],
"new_concepts": [],
"current_concepts": [
"Right Triangle Trigonometry",
"Tangent Ratio"
]
}
</pre_analysis>

<reasoning>

Identify the sides relative to angle A

\[

$$\begin{aligned} &\text{Opposite side} = 5\\ &\text{Adjacent side} = 8\\ &\text{Hypotenuse} = \sqrt{89} \end{aligned}$$

\]

Apply the tangent ratio formula

\[
\tan(A) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{5}{8}
\]
</reasoning>

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

\(\tan(A) =\) <blank>\(\frac{5}{8}\)</blank>
</answer>

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

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Right Triangle Trigonometry",
"Tangent Ratio"
],
"new_concepts": [],
"current_concepts": [
"Right Triangle Trigonometry",
"Tangent Ratio"
]
}
</pre_analysis>

<reasoning>

Identify the sides relative to angle A

\[

$$\begin{aligned} &\text{Opposite side} = 5\\ &\text{Adjacent side} = 8\\ &\text{Hypotenuse} = \sqrt{89} \end{aligned}$$

\]

Apply the tangent ratio formula

\[
\tan(A) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{5}{8}
\]
</reasoning>

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

\(\tan(A) =\) <blank>\(\frac{5}{8}\)</blank>
</answer>

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