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 = 26° and y = 54°, 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

from the figure

angle A = angle x = 26 degrees

angle B = angle y = 54 degrees

third angle = 180 - ( 26 + 54 ) = 100 degrees

b / sin 54 = 5 / sin 100

b = (5 / sin 100 )* sin 54 = 4.10

distance of plane from point A = 4 miles

b) elevation of plane = sin 26 = h / 4

h = 1.75 miles

elevation of plane = 1.75 miles