A pilot is flying over a straight highway He determines the

A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, 5 mi apart, to be x = 28° and y = 52°, as shown in the figure. (Round your answers to two decimal places.)

(a) Find the distance of the plane from point A.
_________ mi

(b) Find the elevation of the plane.

_________ mi

Solution

angle of elevation = 180 - ( 28 + 52 )

= 100 degrees

applying law of sines to find distance of plane from point A

d / sin 52 = 5 / sin 100

d = 5 / sin 100 * sin 52

d = 4

hence, distance of plane from point A = 4 miles

b) elevation of the plane

h / sin 28 = 4 / sin 90

h = 1.88

elevation of plane = 1.88 miles