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4 November, 11:41

A sprinkler head had a 90-degree rotation and shoots 15 feet long. How much area is covered if there are 12 90-degree heads in one yard? How many 90-degree head do you need to cover a 1200 square foot yard?

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  1. 4 November, 11:56
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    A) It can shoot 15 feet long and has a rotation of 90 degrees.

    We can write this area:

    Area = Angle*radius^2

    The radius is 15 ft.

    The angle must be written in radians, so we need to writhe 90° in radians.

    180° is equal to pi.

    Then 90° = (90°/180°) * pi = pi/2

    where pi = 3.14

    Then our area is:

    A = (3.14/2) * (15ft) ^2 = 353.25 ft^2

    B) If we have 12 of those in one yard, we can cover 12 times that area; this is:

    A = 12 * (353.25 ft^2) = 4239 ft^2

    C) Now we want to find the angle such that the covered area for one sprinkler is equal to 1200 ft^2

    Then we can replace it in the equation for the area and get:

    1200ft^2 = angle * (15ft) ^2 = angle*225 ft^2

    angle = 1200/225 = 5.33

    But this is in radians, so we may convert it to degrees.

    We know that 3.14 = 180°

    Then we have

    5.33 rads = (5.33/3.14) * 180° = 305.5°
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