here is a wind turbine.

its blades are arranged in equal thirds of a circle.

the wind turbine rotates through an angle of 2.5 radians.

how many degrees does it turn?

Question

here is a wind turbine.

its blades are arranged in equal thirds of a circle.

the wind turbine rotates through an angle of 2.5 radians.

how many degrees does it turn?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Radian to Degree Conversion" ], "new_concepts": [], "current_concepts": [ "Radian to Degree Conversion" ] } ## Identify the given angle and conversion factor $$ \begin{aligned} &\theta = 2.5\text{ radians}\ &1\text{ radian} = \frac{180^\circ}{\pi} \end{aligned} $$ ## Convert the angle to degrees $$ \begin{aligned} &\theta_{\text{degrees}} = 2.5 \times \frac{180}{\pi}\ &\theta_{\text{degrees}} = \frac{450}{\pi} \approx 143.24 \end{aligned} $$ How many degrees does it turn? $\frac{450}{\pi}$ degrees (or approximately $143.24$ degrees) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Radian to Degree Conversion" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the given angle and conversion factor

Convert the angle to degrees

Answer: