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The minute hand of a clock in a clock tower has a length of 36 inches.

If a butterfly landed on the extreme tip of the minute hand at exactly 12:00 noon and rode the minute hand until 12:45 p.m., how far did the butterfly ride along the arc traced by the minute hand? Round your answer to the nearest foot.

Respuesta :

kemedeiros

Answer:

45 degrees

Step-by-step explanation:

   Butterfly will ride along the arc traced by the minute hand = 14 feet

Perimeter of a sector:

  • Perimeter of a sector of a circle is given by the expression,

         [tex]P=\frac{\theta}{360^\circ}(2\pi r)[/tex]

          Here, θ = Angle formed at the center of the circle by the arc of

                          a sector

                     r = Radius of the circle

Since, minute hand of a clock forms an angle measuring 270° at the center to cover from 12:00 noon to 12:45 p.m.

Length of the minute hand = 36 inches

Perimeter of the arc = [tex]\frac{270}{360}(2\pi)(36)[/tex]

                                  = 169.646 inches

Since, 1 inch = [tex]\frac{1}{12}[/tex] foot

          169.646 inches = 14.137 ft.

                                     ≈ 14 ft.

        Therefore, butterfly will ride 14 feet along the arc traced by minute hand.

Learn more about the perimeter of an arc here,

https://brainly.com/question/1582130?referrer=searchResults

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