Two ropes, ad and bd, are tied to a peg on the ground at point d. the other ends of the ropes are tied to points a and b on a flagpole, as shown below:

angle adc measures 60° and angle bdc measures 30°. what is the distance between the points a and b on the flagpole?

a. 20 feet
b. 15 feet
c. 10 feet
d. 25 feet

So to find the answer you need to use SOHCAHTOA 
Sine= Opposite/ Adjacent
Cosine= Adjacent/Hypotenuse
Tan = opposite/adjacent

angle ADC is 60 so to find the length of line ABC we would use the angle and the line DC. 
We would use Tan with opposite over adjacent
Tan 60 = opp. / 5 root 3 
opp. = 15 
so that is the length of the entire thing, all you need to do now is find the length of the single line of BC which we can use the same equation with just Tan 30 now.
Tan 30 = opp. / 5 root 3 
opp. = 5 
next you need to take the entire ABC length and subtract the length of BC to get AB
15-5 = 10 
so the answer would be C