A circle with a radius of 15 yards contains a sector with an area of 609 yde. Find the measure of the central angle of the sector in b

Question

A circle with a radius of 15 yards contains a sector with an area of 609 yde. Find the measure of
the central angle of the sector in both radians and degrees.

(HELP PLEASE)(WILL GIVE BRAINLIEST)

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Edana Edana 5 years 2021-08-21T03:55:04+00:00 1 Answers 10 views 0

Answers ( )

  1. thucuc
    0
    2021-08-21T03:56:56+00:00
    Reply

    Answer: 310.3° or 5.41 radians.

    Step-by-step explanation:

    The area of a circle of radius R is calculated as:

    A = pi*R^2

    Now, if we have a sector of an angle θ degrees, the area of that sector is:

    A = (θ/360°)*pi*R^2

    In this case, we know that:

    R = 15yd

    And the area of the sector is 609 yd^2

    Then we can replace these two values in the equation to get:

    609yd^2  =(θ/360°)*3.14*(15yd)^2

    (609yd^2)*360°/(3.14*(15yd)^2) = θ = 310.3°

    And we want the angle also in radians.

    We know that:

    3.14 rad = 180°

    (3.14 rad/180°) = 1

    Then:

    310.3° = 310.3°*(3.14 rad/180°) = (310.3°/180°)*3.14 rad = 5.41 radians.

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