



 
Ray, Draw a diagram. A is the airplane, P is the point on the surface of the Earth directly below the plane, h is the altitude of the plane, R is the radius of the earth, H is the point where the line of sight hits the horizon, C is the centre of the Earth and H is the height of the cap of the Earth which defines the visible surface region. The surface area is given by
Since R is a constant
What remains is to find dH/dt. Triangle BCH is a right triangle. Use a trig function to write an expression relating R, H and θ. Use triangle ACH to write an expression relating R, h and θ. Solve these two expression to find a relationship relating R, H and h, and differentiate with respect to t. Harley  


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