Answer:
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)
