the radius of circle c is 16 units long. find the lenght of an arc that has a measure of 270. round to the nearest hundreth. i need to answer this question. i don't want the answer but i was wondering if someone could give me the formula i need to set this up.
did you mean the arc with a central angle of 270 degrees ?
if so, find the circumference which is 2pi(16)
then take 3/4 of that
since 270 degrees is 3/4 around the circle.
thats exactly what i needed. thank you very much
To find the length of an arc, the formula you need to use is:
Arc Length = (Angle / 360) x (2πr)
Where:
- Angle is the measure of the angle (270 in this case)
- r is the radius of the circle (16 units in this case)
- π is a mathematical constant approximately equal to 3.14159
Using this formula, you can calculate the length of the arc.
To find the length of an arc with a given measure, you can use the formula:
Arc Length = (arc measure / 360) x (2πr)
In this formula:
- Arc Length represents the length of the arc.
- Arc measure represents the measure of the arc (in degrees).
- r represents the radius of the circle.
- π (pi) is a mathematical constant approximately equal to 3.14159.
In your case, the radius of the circle is given as 16 units, and the arc measure is 270 degrees. Let's substitute these values into the formula:
Arc Length = (270 / 360) x (2π x 16)
Simplifying further:
Arc Length = (0.75) x (2π x 16)
Now, you can calculate the length of the arc by multiplying:
Arc Length = 0.75 x 2 x 3.14159 x 16
Arc Length = 0.75 x 6.28318 x 16
Arc Length ≈ 75.39822 units (rounded to the nearest hundredth)
Therefore, the length of the arc with a measure of 270 degrees and a radius of 16 units is approximately 75.40 units.