A plane is flying 2000 feet above sea level toward a mountain as shown. The pilot observes the top of the mountain to be α = 17 ∘ above the horizontal, then immediately flies the plane at an angle of β = 19 ∘ above horizontal. The airspeed of the plane is 100 mph. After 5 minutes, the plane is directly above the top of the mountain. How high is the plane above the top of the mountain (when it passes over)? What is the height of the mountain? Round to the nearest 10 feet.