In quadrilateral ABCD, sides AB and BC both have length 10, sides CD and DA both have length 17, and the measure of angle ADC is 60∘. What is the length of diagonal AC?
[asy]draw((0,0)--(17,0));
draw(rotate(301, (17,0))*(0,0)--(17,0));
picture p;
draw(p, (0,0)--(0,10));
draw(p, rotate(115, (0,10))*(0,0)--(0,10));
add(rotate(3)*p);draw((0,0)--(8.25,14.5), linetype("8 8"));label("A", (8.25, 14.5), N);
label("B", (-0.25, 10), W);
label("C", (0,0), SW);
label("D", (17, 0), E);[/asy]<spanclass=′latex−bold′>(A)</span>13.5<spanclass=′latex−bold′>(B)</span>14<spanclass=′latex−bold′>(C)</span>15.5<spanclass=′latex−bold′>(D)</span>17<spanclass=′latex−bold′>(E)</span>18.5