find the length of the arc intercepted by a central angle of 35 degree 28' in a circle of radius 15ft....i cant figure out how to get it ??
C = 2pi*r = 6.28 * 15 = 94.2 Ft. =
Circumference = Total distance around the circle. The intercepted arc is a fraction of that distance:
L = (35.47/360) * 94.2 = 9.28 Ft.
To find the length of the arc intercepted by a central angle in a circle, you can use the formula:
Arc Length = (Central Angle / 360 degrees) * (2πr)
In this case, the central angle is 35 degrees 28 minutes. To calculate the angle in decimal degrees, convert the minutes to degrees by dividing by 60:
35 degrees + (28 minutes / 60 minutes/degree) = 35.467 degrees
Now, you have the central angle in decimal degrees. The radius of the circle is given as 15 feet. Substituting into the formula:
Arc Length = (35.467 degrees / 360 degrees) * (2π * 15 feet)
First, convert degrees to radians:
35.467 degrees * (π / 180 degrees) = 0.619 radians
Now substitute into the formula:
Arc Length = (0.619 radians / 360 degrees) * (2π * 15 feet)
Simplify:
Arc Length = (0.619 / 360) * (2π * 15 feet)
Now, calculate:
Arc Length ≈ 0.086 * (2π * 15 feet)
Arc Length ≈ 4.07 feet (rounded to two decimal places)
Therefore, the length of the arc intercepted by a central angle of 35 degrees 28 minutes in a circle with a radius of 15 feet is approximately 4.07 feet.