Find x using the picture below.

  X = 60

Step-by-step explanation:

Considering that the radius of the circle is 11 ( a ), we need to add that to 50  in order to get the full hypotenuse ( c ).

Using the Pythagorean theorem, " a^2 + b^2 = c^2 ", we can substitute our given variables.

The result would be ( 11 )^2 + b^2 = ( 61 )^2  

                              or  ( 121 ) + b^2 = ( 3721 )

Subtract a from both sides to get b^2 = 3600

And finally, square root our answer to get b = 60

Since b is x on our chart, the answer will be x = 60

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

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.