The arc corresponding to a central angle of 35 degrees in a circle of radians 10 feet measures _____ feet. Round your answer to two decimal places.
Surely, you meant:
"...in a circle of radius 10 feet... "
arc = rØ, where Ø is in radians
so convert 35° to radians and plug in
or , use a ratio
35°/360° = arc/circumference
etc
6.11
To calculate the length of an arc in a circle, you can use the formula:
Arc length = (central angle / 360 degrees) * (2 * pi * radius)
Given the central angle is 35 degrees and the radius is 10 feet, we can substitute these values into the formula:
Arc length = (35 degrees / 360 degrees) * (2 * pi * 10 feet)
Simplifying further:
Arc length = (35/360) * (20 * pi) feet
Arc length = (7/72) * (20 * pi) feet
Arc length = (7/18) * pi feet
Calculating the approximate value:
Arc length ≈ 3.88 feet
Therefore, the arc corresponding to a central angle of 35 degrees in a circle with a radius of 10 feet measures approximately 3.88 feet.
To find the length of the arc corresponding to a central angle of 35 degrees, you can use the formula:
Arc length = (central angle / 360 degrees) * (circumference of the circle)
First, let's convert the central angle from degrees to radians, since the given circle is in radians.
Radians = (degrees * π) / 180 degrees
Radians = (35 degrees * π) / 180 degrees
Radians ≈ 0.61 radians (rounded to two decimal places)
Next, we calculate the circumference of the circle using the formula:
Circumference = 2 * π * radius
Since the radius is not given, we'll assume it to be 10 feet, as mentioned in the question.
Circumference = 2 * π * 10 feet
Circumference ≈ 62.83 feet (rounded to two decimal places)
Now we can substitute the values into the arc length formula:
Arc length = (0.61 radians / 360 degrees) * 62.83 feet
Arc length ≈ 0.107 feet (rounded to two decimal places)
Therefore, the arc corresponding to a central angle of 35 degrees in a circle of radius 10 feet measures approximately 0.11 feet (rounded to two decimal places).