Don't you just love related rates?

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SUMMARY

The discussion centers on solving a related rates problem involving the angle of elevation of the Sun and the length of the shadow cast by a 400-ft-tall building. The angle is decreasing at a rate of 0.25 rad/h when the angle of elevation is π/6. The correct approach involves using the equation L = H cot(θ) and differentiating it to find the rate of change of the shadow's length. This method effectively relates the variables and their rates of change.

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ms. confused
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The angle of elevation of the Sun is decreasing at a rate of 0.25 rad/h. How fast is the shadow cast by a 400-ft-tall building increasing when the angle of elevation of the Sun is π/6?

I thought about using the special triangle to find exact values for trig functions at π/6 but I don't know which equation I should use to relate the rate of change. What should I do? :rolleyes:
 
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Just write [itex]L = H \cot \theta[/itex] with the obvious definitions and differentiate.
 

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