Ask Question
12 November, 11:11

Ashley maintains a circular flower garden that has a radius of 25 feet. She would like to construct a fence around most of the garden. She wants to keep an opening to the garden that makes a central angle of 30 degrees. How long, to the nearest foot, does the fence need to be?

+3
Answers (1)
  1. 12 November, 14:57
    0
    The fence need to be 144 feet length

    Step-by-step explanation:

    1. Let's review the information given to us to answer the question correctly:

    Radius (r) of the circular garden = 25 feet

    Measurement of the angle to the garden = 30°

    2. How long, to the nearest foot, does the fence need to be?

    Let's recall that the formula of the circumference is:

    c = 2πr

    Upon saying that, let's also recall that the circumference of a circle is the length of the 360 degree arc of that circle. Since we know that the circumference of a 360 degree arc is 2Πr, we can calculate the length of various arcs of a circle, provided that we know the radius of such a circle. The length of an arc of n degrees equals (n/360) times the circumference. In our question, n = 330 because Ashley wants to maintain an opening of a central angle of 30 degrees.

    x = Length of the fence

    π = 3.1416

    Now, we can solve for x, this way:

    330/360 = x/50π

    360x = 330 * 50π

    360x = 330 * 157.08

    360x = 51,836.4

    x = 51,836.4/360

    x = 143.99 or 144 (rounding to the nearest foot)
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Ashley maintains a circular flower garden that has a radius of 25 feet. She would like to construct a fence around most of the garden. She ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers