Question 70998
You could use the law of cosines to solve this problem since you have two sides of a triangle and the included angle. Let the two known sides be a (12 miles) and b (7 miles). You want to find the length of the third side (c).  The included angle is C = 35 degrees. The law of cosines is:
{{{c^2 = a^2+b^2-2abcos(C)}}} Substituting the given values of a(12), b(7), and angle C(35):
{{{c^2 = 12^2 + 7^2 - 2(12)(7)cos(35)}}} Simplify.
{{{c^2 = 144 + 49 - 168cos(35)}}}
{{{c^2 = 193 - 168(0.82)}}}
{{{c^2 = 193-137.62}}}
{{{c^2 = 55.38}}} Take the square root of both sdes.
{{{c = 7.44}}}
The two objects are approximately 7.44 miles apart.