Trig circle sectors? Finding arc length?

Given a circle with center O. The area of sector AOB is 9x/2 and the measurement of angle AOB is 45 degrees.

What is the radius of circle O?

What is the arc length off AB. IN TERMS OF PI!!

NEED HELP THANK YOU.

would appreciate working.

3 Answers

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  • Anonymous
    1 decade ago
    Favorite Answer

    The area of a sector given the radius of the circle (r) and the angle that subtends the sector in radians (θ) is given by:

    A = (1/2)θr^2.

    With A = 9x/2 and θ = π/4 (since 45° = π/4 radians), we have:

    9x/2 = (1/2)(π/4)r^2

    ==> 9x/2 = πr^2/8

    ==> 36x = πr^2

    ==> r^2 = 36x/π

    ==> r = 6√(x/π).

    Then, the length of AB is just s = rθ = 3√(x/π)/2 units.

    I hope this helps!

  • 5 years ago

    area of a circle pi r^2 180 degrees corresponds to half circle area of a cirle with r =10 is A = pi (10)^2 = 100 pi ft^2 area corresponding to an arc length of 180 degrees is = 50 pi ft^2 (approx = 157 ft^2)

  • Ed I
    Lv 7
    1 decade ago

    A = (1/2)r^2 θ

    9x/2 = (1/2) r^2 (π/4)

    36/π = r^2

    6/√π = r

    r = 3.385137501... ≈ 3.385

    s = r θ ≈ 3.385 (π/4) = 0.8462843753...π ≈ 0.846π

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