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?

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)