We apply trigonometry and using the attached illustration, we know that sine of an angle is the ratio of opposite to hypotenuse. In this case, the hypotenuse is the diagonal in question.
Sin 30°=10/hypotenuse
Hypotenuse=10/sin30°=10/0.5=20 miles
Therefore, the plane has gone a diagonal distance equivalent to 20 miles from its take off position