Problem #1
Find the arc length corresponding to the given angle (in degrees) on a circle of radius 3.3.
An angle of 39 degrees has an arc length of_______ units.
Problem #2
The diameter of the wheels on your car (including the tires) is 25 inches. You are going to drive 295 miles today. Each of your wheels is going to turn by an angle of_________degrees.
C = pi*D = 3.14 * 25 = 78.5 in.
5,280ft/mi * 12in/ft. * 360o/78.5in * 295mi =
Problem #1:
To find the arc length corresponding to a given angle on a circle, we can use the formula:
Arc length = (angle / 360) * 2 * π * radius
Given that the radius of the circle is 3.3 units and the angle is 39 degrees, we can substitute these values into the formula:
Arc length = (39 / 360) * 2 * π * 3.3
Simplifying the calculation:
Arc length = (0.1083) * 2 * π * 3.3
Arc length ≈ 0.6078 * 6.283 * 3.3
Arc length ≈ 3.7825 units
Therefore, an angle of 39 degrees corresponds to an arc length of approximately 3.7825 units.
Problem #2:
To find the angle in degrees that each wheel is going to turn when driving a certain distance, we need to use the formula:
Angle (in degrees) = (Distance / Circumference) * 360
Since the diameter of the wheel is given as 25 inches, the circumference can be calculated as:
Circumference = π * diameter
Substituting the value of diameter as 25 inches:
Circumference = 3.1416 * 25
Circumference ≈ 78.54 inches
Now, to find the angle, we can substitute the values of distance and circumference into the formula:
Angle (in degrees) = (295 miles * 5280 feet/mile * 12 inches/foot) / 78.54 inches * 360
Simplifying the calculation:
Angle (in degrees) = (295 * 5280 * 12) / 78.54 * 360
Angle (in degrees) ≈ 183621600 / 28234.4
Angle (in degrees) ≈ 6509.17 degrees
Therefore, each wheel is going to turn by an angle of approximately 6509.17 degrees.