1. The angles of elevation to an airplane from two points A and B on level ground are 55° and 72°, respectively. The points A and B are 2.2 miles apart, and the airplane is east of both points in the same vertical plane.
(a) Draw a diagram that represents the problem. Show the known quantities on the diagram.
(b) Find the distance between the plane and point B.
(c) Find the altitude of the plane.
(d) Find the distance the plane must travel before it is directly above point A.
2. A flagpole at a right angle to the horizontal is located on a slope that makes an angle of 12° with the horizontal. The flagpole's shadow is 16 meters long and points directly up the slope. The angle of elevation from the tip of the shadow to the sun is 20°.
(a) Draw a diagram that represents the problem. Show the known quantities on the diagram and use a variable to indicate the height of the flagpole.
(b) Write an equation that you can use to find the height of the flagpole.
(c) Find the height of the flagpole.