1998 AHSME Problem 19

How many triangles have area 10 and vertices at (-5,0),(5,0) and (5\cos \theta, 5\sin \theta) for some angle \theta?

\mathrm{(A) \ }0 \qquad \mathrm{(B) \ }2 \qquad \mathrm{(C) \ }4 \qquad \mathrm{(D) \ }6 \qquad \mathrm{(E) \ } 8

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.