find the arc length of AB to the nearest tenth. AB equals 45 degrees. radius is 5 in.
45 degrees is 1/8 of a circle.
arclength=1/8 * 2PI*radius
To find the arc length of AB, you can use the formula:
Arc Length = (Central Angle / 360) * (2 * π * r)
Where:
- Central Angle is the angle subtended by the arc in degrees.
- r is the radius of the circle.
In this case, the central angle AB is given as 45 degrees, and the radius (r) is given as 5 inches. Now we can plug these values into the formula to calculate the arc length.
Arc Length = (45 / 360) * (2 * π * 5)
Simplifying the expression further:
Arc Length = (1/8) * (2 * 3.14159 * 5) ≈ 0.19634954084936207 * 31.41592
Arc Length ≈ 6.183 inches
Therefore, the arc length of AB is approximately 6.183 inches (rounded to the nearest tenth).