2. Or, multiply the degrees in the given arc by the radius of the circle, and the product by ·01745 for the length of the arc.
Example.—Rule 2.—Required the length of an arc of 30°, the radius being 9 feet.
30 × 9 × ·01745 = 4·7115. Length of arc.
To find the area of the sector of a circle.
Multiply the radius by the arc, and half the product will be the area.
Example.—Required the area of the sector, whose radius is 30 inches, and the length of the arc 36·6 inches.
36·6 × 30 2 = 549 square inches. Area required.
To find the area of the segment of a circle.
Find the area of the sector, by the preceding rule. Then find the area of the triangle formed by the chord of the segments, and the radii of the sector. Then, if the segment be less than a semicircle, subtract the area of the triangle from it; or, if the segment be greater than a semicircle, add the area of the triangle to it; for the area of the segment.