An arc of length 30 meters is formed by a central angle A on a circle of radius 15. The measure of A in degrees (to the nearest minute) is
arc= angleinRadians*r
angleinRadians=arc/r=2
angleindegrees=180*2/PI=114.591559
114 degrees, and .591558*60 minutes
114 deg, and 35min
To find the measure of angle A in degrees, we can use the formula relating the length of an arc to the circumference of the circle and the measure of the central angle.
The formula is:
Arc length = (angle A / 360) * (2 * π * radius)
Here, the arc length is given as 30 meters, and the radius of the circle is given as 15.
Substituting the values into the formula, we get:
30 = (A / 360) * (2 * π * 15)
Next, let's solve for A:
Multiply both sides by (360 / (2 * π * 15)):
A = 30 * (360 / (2 * π * 15))
Simplifying further:
A = 30 * (12 / π)
To find the measure of angle A in degrees, we can evaluate the expression:
A ≈ 109.0967 degrees
Therefore, the measure of angle A in degrees, to the nearest minute, is approximately 109 degrees.