Question

1. What is the measure in radians for the central angle of a circle whose radius is 6 cm and intercept arc length is 5.4 cm?

Make sure to show all calculations.

2. In a circle with a radius of 26.9 m, an arc is intercepted by a central angle of 9π59π5 radians.

What is the arc length?

Use 3.14 for ππ and round your final answer to the nearest hundredth.

Make sure to show your calculations

Answer 1

Hello!

1.
find circumferece
c=2pir
c=2*6*pi=12pi
intercept is 5.4

2pi radians=all

part/whole=part/whole
5.4/12pi=x/2pi
times both sides by 12pi
5.4=6x
divide both sides by 6
0.9=x
answer is 0.9 radians



2.
assuming 9pi/5 radians

find circumference
c=2pir
c=2*26.9*pi
c=53.8pi

arc/circumference=(9pi/5)/2pi

x/(53.8pi)=(9pi/5)/(2pi)
x/(53.8pi)=18/5
times both sides by 53.8pi
x=608.46266 m
about x=608.46 m


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