Imagine an expanding right triangle. If one leg has a fixed length of {{MATH_126}} m, one leg is increasing with a rate of {{MATH_127}} m/s, and the hypotenuse is expanding to accommodate the expanding leg, at what rate is the angle opposite the fixed leg changing when both legs are {{MATH_128}} m long? {{CMD_129}} First, we {{CMD_130}}introduce the variables{{CMD_131}} {{MATH_132}}, {{MATH_133}}, {{MATH_134}}, as in the previous example, and {{MATH_135}}, denoting the angle opposite the leg with fixed length. We {{CMD_136}}identify{{CMD_137}} the given rate {{MATH_138}} m/s and the unknown rate {{MATH_139}}, when {{MATH_140}}. Next, we {{CMD_141}}draw a picture{{CMD_142}}. {{CMD_143}} {{ENV_144}} {{CMD_145}}