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Answer :
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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Rewritten by : Barada
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
