For each of the following angles, assume that the terminal ray of the angle opens up in the counter-clockwise direction a.

a) a circle with a radius 8 cm long is centered at angle a's vertex, and angle a subtends an arc length of 88 cm along this circle.

-the subtended arc is how many times as long as the circle's radius?

- therefore, the radian measure of angle a is?

b) a circle with a radius 18 cm long is centered at angle b's vertex, and angle b subtends an arc length of 72 cm along this circle. what is the radian measure of angle b?

c) a circle with a radius 3 inches long is centered at angle c's vertex, and angle c subtends an arc length of 1.1781 inches along this circle. what is the radian measure of angle c?

a) The subtended arc is 11 times longer than the radius.

ii. Angle A, subtended by the arc is 11 rad.

b) Angle B, subtended by the arc is 4 rad.

c) Angle C, subtended by the arc is 0.39 rad.

Step-by-step explanation:

a) From the question, the radius of the circle is 8 cm and length of the arc is 88cm.

length of an arc can be determined by;

              length of an arc     = (θ/2) × 2r

where: r is the radius and θ is the angle subtended by the arc in radians.

So that;

                    length of an arc = θr

                                          88 = 8θ

                                         ⇒ θ = 11

        ∴           length of an arc = 11r

The subtended arc is 11 times longer than the radius.

ii. Angle A, subtended by an arc,  θ=

        ⇒                  θ =

                                =

                                = 11 rad

Angle A, subtended by the arc is 11 rad.

b) Angle B, subtended by an arc =  

       ⇒                   θ =

                                 =

                                 = 4 rad

Angle B, subtended by the arc is 4 rad.

c) Angle C, subtended by an arc =  

          ⇒                   θ =

                                    =

                                    = 0.39 rad

Angle C, subtended by the arc is 0.39 rad.

answer;

the correct answer

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have a nice day < 3