trig
posted by Barb on .
angles of elevation to an airplane are measured from the top and the base of a building that is 40 m tall. The angle from the top of the building is 31°, and the angle from the base of the building is 40°. Find the altitude of the airplane. (Round your answer to two decimal places.)

measured from the plane, the building subtends an angle of 9°
the distance d from the top of the building to the plane is found by
d/sin50° = 40/sin9°
d = 195.87
now, knowing d, the height h of the plane can be found:
(h40)/d = sin31°
(h40)/195.87 = sin31°
h = 40 + 195.87 sin31°
h = 140.88
h =