find the length of the major arc. write your answer using \pi\ with no spaces.

$\text{length}_{\text{arc}} = $ $\text{ft}$

Question

find the length of the major arc. write your answer using \pi\ with no spaces.

$\text{length}_{\text{arc}} = $   $\text{ft}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Arc Length Formula" ], "new_concepts": [], "current_concepts": [ "Arc Length Formula", "Central Angle Measure" ] } ## Identify the given parameters $$ \begin{aligned} r &= 12\text{ ft} \ \theta &= 315^\circ \end{aligned} $$ ## Apply the arc length formula $$ \begin{aligned} s &= 2\pi r \cdot \frac{\theta}{360^\circ} \ s &= 2\pi (12) \cdot \frac{315}{360} \end{aligned} $$ ## Simplify the expression $$ \begin{aligned} s &= 24\pi \cdot \frac{7}{8} \ s &= 3\pi \cdot 7 \ s &= 21\pi \end{aligned} $$ Find the length of the major arc. Write your answer using "pi" with no spaces. $\text{Length}_{\text{arc}} =$ 21pi ft { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Arc Length Formula" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given parameters

Apply the arc length formula

Simplify the expression

Answer: