Now we {{CMD_278}}find equations{{CMD_279}} that relate the variables {{MATH_280}} and {{MATH_281}}. We use the fact that we have similar triangles to write: {{ENV_282}} Since {{MATH_283}} and {{MATH_284}} are both functions of time, we {{CMD_285}}differentiate{{CMD_286}} both sides of the equation above. We use implicit differentiation and write {{MATH_287}} At this point we {{CMD_288}}evaluate{{CMD_289}} all the quantities at time when {{MATH_290}} ft {{MATH_291}} Now we {{CMD_292}}solve{{CMD_293}} for {{MATH_294}} and get that {{MATH_295}}, when {{MATH_296}} ft. Therefore, the shadow is growing at a rate of {{MATH_297}} ft/s when the person is {{MATH_298}} ft from the lamp.{{CMD_299}} {{CMD_300}} {{CMD_301}}