Construct a trapezium, ABCD to represent this question;
AD and CB are parallel and horizontal, BD is vertical and represents the height of the plane, A and D are on the ground with the woman positioned at A.
angle DAB =ABC (Z angles) is 6 degrees, and DAC is 15 degrees, making BAC = 15-6 =9 degrees
distance travelled by the plane in 6 minutes BC, is 400*6/60 = 40 miles
using the sine formula AC/sine6 = CB/sine9 ; AC = 40 *0.1045/0.1564 = 26.73 miles
drop a vertical line from C to a point X on AD; CX = BD (opposite sides of a rectangle)
CX/AC = sine15; therefore CX = 26.73 * 0.2588 = 6.92 miles = BD, or the height of the plane.
Hence the height of the plane is 6.92 miles