Bob is training for a race. bob ran 14.6 miles away from his home. then, bob ran 9.8 miles towards his home. finally, bob ran 5.3 miles away from his home. how far is bob from his home?
This equation is a matter of doing addition and subtraction in the right order. You start with 14.6, because that is how far he is away from his home. Then, you subtract 9.8 because he's coming towards his home, and he is now 4.8 miles away from his home. Finally add 5.3 because he runs away this time, and you end up with Bob is 10.1 miles away from his home. Guess he'd better start running back!
x = central angle apc = measure of minor arc ac
the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.
what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)
c = circumference
c = pi*d
c = pi*24
c = 24pi
now multiply this by 5/12 to get
distance along minor arc ac = (5/12)*(circumference)
distance along minor arc ac = (5/12)*(24pi)
distance along minor arc ac = 10pi
the formula you can use is
l = (x/360)*pi*d
l = length of minor arc
x = central angle
d = diameter
which essentially is the steps we took though a bit differently.
the answer is 96 degrees
you have to realize that a line equals 180 degrees