Original
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}}