Radian and Degree Measure

Question

Find the arc-length of the sector of a circle with the given radius r and central angle θ. Give the answer in the given unit of measure, rounded to the nearest hundredth.

r = 51 in.; θ = 5π/4

____in.

Answer 1

arc length = radius times radians = 51(5pi/4) = 255pi/4 = 63.75pi inches

= about 200.28 inches rounded to 2 decimals

and if you're interested

sector area = half radians times radius squared

A = .5theta(r^2) = .5(51)^2(5pi/4) = (5pi/8)2601)= 13,005pi/8 square inches

= about 5,107..05 in^2

Answer 2

s = rθ, in radians

Can you substitute and answer?