When Satellites Observe Earth, They Can Scan Only Part of Earth's

Multiple Choice

When satellites observe Earth, they can scan only part of Earth's surface. Some satellites have sensors that can measure the angle $\theta$ shown in the figure. Let $h$ represent the satellite's distance from Earth's surface and let $r$ represent Earth's radius. Find the rate at which $h$ is changing with respect to $\theta$ when $\theta = 60 ^ { \circ }$ (Assume $r = 4460$ miles.) Round your answer to the nearest unit.

A) $- 2973 \mathrm { mi } / \mathrm { radian }$
B) $- 5150 \mathrm { mi } / \mathrm { radian }$
C) $5150 \mathrm { mi } / \mathrm { radian }$
D) $- 8920 \mathrm { mi } / \mathrm { radian }$
E) $2973 \mathrm { mi } / \mathrm { radian }$