Find the measure of arc length ab.

Question

A circle with a radius of 8 and a chord measuring at 10.

Answer 1

If you draw a circle with a radius of 8, then draw a chord parallel to that radius, you could draw the line of the radius from the center of the circle to each of the chord's endpoints, forming an isosceles triangle, as the radius lines are both length 8, and the last side being that of the chord, length 10.

If we position this chord to bisect the triangle into two right triangles, the angle of the bisecting line and either radius of 8 will be half of the arc's angle length. With that, we know the hypotenuse (8) and the opposite side (10 / 2 = 5) and we can use sin a = 5 / 8: a = arcsin 5/8 = 38.7 degrees

Now, we have half of the angle of the arc length. Doubling it, we get 77.4 degrees.

Arc Length equation is s = r(theta, or angle) = 8 x 77.4 degrees (or 77.4 / pi = .43 radians) = 3.44

Hope this helps!