Whenworkingwith anglesmeasuredin degrees,we oftenreportour answersusinga decimal,suchas
78.5
o
. However, in somecontexts,anglesare measuredusingfractionalparts.
Measuringangles
Example3:Two wheelsare in directcontact.The radiusof one is .5 meters.The radiusof the otheris 1
meter. The smallerone rotatesfour full turns.How manyrotationsdoesthe largerwheelmake?How many
degreesdoesthe largerwheelrotatethrough?
Solution:Everytime the smallwheelrotatesonce,its entirecircumferencepassesalongthe largerwheel,
Sincethe circumferenceof the largewheelis the largewheelrotateshalf way around.So if the smallwheelrotates4 times,or 360 x 4 = 1440othe largewheelrotates2 times,or 360 x 2 = 720o.
We can measureanglesin muchthe sameway we measuretime.Aminuteis of a degree.Asecond
is of a minute,so it is of a degree.For example, 48 o20'45"is the way we write48 degrees, 20
minutes,and 45 seconds.We can writethis angleusingfractionnotation,as well as decimalnotation:
We can also writea decimaldegreeusingdegrees,minutes,and seconds.For example,we can rewrite
125.88oif we writethe decimalpart as a fraction:
Now solveforx:
Now we have125.88o= 125o52.8'.We needto write.8 minutesas seconds: