a) find the radian and degree measures of the certeral angle θ subtended by the given arc length s on a cricle of radius r (r=20in & s=3ft) b) find the are of the sector determined by θ

Answer 1

s = 3 ft

s = 36 in

s = 1.8 radians (36/20)θ

θ = 1.8 r

Locate the formula for conversion of radians to degrees and the formula for the area of a sector.

Answer 2

A radian is, in a sense, a measure of how many radii we've walked around a circle: on a circle with a radius of 3, for instance, an arc length of 6 subtends an angle of 2 radians, since 6 = 3 · 2. A general way of expressing that fact is that

s = rθ, where s is the arc length, r is the circle's radius, and θ is the measure of the subtended angle in radians.

For ease of calculation, let's convert everything to inches, so r = 20 and s = 3 · 12 = 36. Using these values in the above formula gives us the equation 36 = 20θ, and dividing both sides by 20 gives the value of θ = 36 / 20 = 9/4 = 2.25 radians