How do you convert #(5pi)/7# into degrees?

1 Answer
Aug 3, 2015

you need to use the conversion #pi=180# to get the answer

Explanation:

#(5*pi)/7# is a radian measure which needs to be converted to degrees. For that we need a simple conversion factor: #pi=180#

Now we are going to setup an equation with the conversion factor. A nice way to do this is to take advantage of the proportionality of the problem. So we set the equations up like this:

#(5*pi)/7=x# in the same proportion as #pi=180#

#(5*pi)/7/pi=x/180#

we want to simplify this by changing the division to a multiplication

#(5*pi)/7*(1/pi)=x/180#

now we simplify the #pi/pi = 1#

#5/7=x/180#

to solve we simply undo the division on x with a multiply

#180*(5/7)=x#

#x=900/7=128.571#
(we changed the direction at the end to follow convention)

NOTE: always put the same units in the same fraction
#(rad)/(rad)=(degrees)/(degrees)#

and that makes us happy. :)