Distance to Earth From an exterior point P that is h units from a circle of radius r, a ta...

Distance to Earth From an exterior point P that is h units from a circle of radius r, a tangent line is drawn to the circle (see the figure). Let y denote the distance from the point P to the point of tangency T.

(a) Express y as a function of h. (Hint: If C is the center of the circle, then PTis perpendicular to CT.)

(b) If r is the radius of Earth and h is the altitude of a space shuttle, then y is the maximum distance to Earth that an astronaut can see from the shuttle. In particular, if h =200 mi and r ≈4000 mi, approximate y.

EXERCISE