Anonymous
Anonymous asked in Science & MathematicsMathematics · 6 months ago

Circle Geometry Math Problem Help? (diagram attached)?

A man designs a garden as shown. From point D outside the circle with centre C, two tangents, DA and DB, each 12 ft in length, meet the radius of the circle at points A and B respectively. Determine the total area of the man's garden.

Attachment image

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  • Mike G
    Lv 7
    6 months ago
    Favorite Answer

    tan θ = 12/5

    2θ = 134.76°

    Central Reflex Angle = 360-134.76 = 225.24°

    = 225.24π/180 radians

    Area of circular part = 0.5*25*225.24π/180

    = 49.14 ft^2

    Area of the two triangles = 60 ft^2

    Total Area = 109.14 ft^2

  • 6 months ago

    The area of the two triangle sections is easy to figure out. They are right triangles, so they each have an area of ½(5*12) = 30 ft² for a total of 60 ft².

    So we just need the larger sector ACB.

    Start by figuring out the angle θ using trigonometry:

    tan θ = 12/5

    θ = arctan(12/5)

    θ = 67.38°

    That means the central angle for the outside sector ACB is:

    360° - 2θ

    ≈ 360° - 2 * 67.38°

    ≈ 225.24°

    Now just take the full circle (π5² = 25π sq. ft.) and take the fraction for the sector.

    Asector = (225.24 / 360) * 25π

    Asector ≈ 39 sq. ft.

    Add the 60 sq. ft. we previously calculated for the triangles.

    Answer:

    ~99 sq. ft.

    Attachment image
    • Puzzling
      Lv 7
      6 months agoReport

      I'm not sure where my calculator messed up. Maybe I copied 39 instead of 49. Anyway, the method was correct, sorry about the calculation mistake.

  • Anonymous
    6 months ago

    Do it yourself. We're not gonna do your fuсking homework for you.

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