Question: An Earth-observing satellite can see only a portion of the Earth's surface. The satellite has horizon sensors that can detect the angle \(\theta\) shown in the accompanying figure. Let \(r\) be the radius of the Earth (assumed spherical) and \(h\) the distance of the satellite from the Earth's surface.

1. Show that \(h=r(\csc \theta-1)\).
2. Using \(r=6378 \mathrm{~km}\), find the rate at which \(h\) is changing with respect to \(\theta\) when \(\theta=30^{\circ} .\) Express the answer in units of kilometers/degree.

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