A subtending arc on a circle with a radius of 4.5 centimeters has an arc length of 8π. The measure of the angle subtended by the arc is ?

Question

A subtending arc on a circle with a radius of 4.5 centimeters has an arc length of 8π. The measure of the angle subtended by the arc is ?

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Genesis 1 month 2021-10-18T17:22:13+00:00 1 Answer 0 views 0

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    2021-10-18T17:23:25+00:00

    Answer: 320°

    Step-by-step explanation:

    This is a circle geometry.

    The arc length of the circle is given to be 8πcm and the radius is 4.5cm.

    Now the length of an arc of a circle is

    Arc length = πr0°/180° or 2πr0°/360°

    To find the angle 0° subtend at the center we equate the arc length with the formula and solve for 0°.Now we go

    πr0°/180 = 8π, convert to a simple linear equal and solve for the angle.

    πr0° = 8π × 180

    0°. = 8π × 180

    ———–

    π × r

    = 8 × 180. 8 × 180

    ——– or ———

    9/2. 4.5

    = 8 × 180 × 2

    ————

    9

    = 8 × 20 × 2

    = 320°

    or 8 × 180/4.5

    = 1440/4.5

    = 320°

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