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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?

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Answer:

a) 11            θ = 11

b) 4             θ = 4

c) 0.3927   θ = 0.3927

Step-by-step explanation:

a) r = 8 cm      length  =  88 cm    Then

The subtended arc is 11 times as long as the circle radius

the radian measure angle A is 11

b)  r = 18 cm    length = 72 cm  

The subtended arc is 4 times as long as the circle radius

the radian measure angle A is 4

c)   r = 3 in       length  = 1.1781 in

The subtended arc is 0.3927 times as long as the circle radius

the radian measure angle A is 0.3927

olayemiolakunle65

Answer:

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[tex]\pi[/tex]) × 2[tex]\pi[/tex]r

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= [tex]\frac{length of the arc}{radius}[/tex]

        ⇒                  θ = [tex]\frac{s}{r}[/tex]

                                = [tex]\frac{88}{8}[/tex]

                                = 11 rad

Angle A, subtended by the arc is 11 rad.

b) Angle B, subtended by an arc =  [tex]\frac{length of the arc}{radius}[/tex]

       ⇒                   θ = [tex]\frac{s}{r}[/tex]

                                 = [tex]\frac{72}{18}[/tex]

                                 = 4 rad

Angle B, subtended by the arc is 4 rad.

c) Angle C, subtended by an arc =  [tex]\frac{length of the arc}{radius}[/tex]

          ⇒                   θ = [tex]\frac{s}{r}[/tex]

                                    = [tex]\frac{1.1781}{3}[/tex]

                                    = 0.39 rad

Angle C, subtended by the arc is 0.39 rad.

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