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## Homework Statement

A man walks along a straight path at 5km/hr. A search light is located on the ground

30 metres form the path and is kept focused on the man. At what rate is the searchlight

rotating when the man is 20 metres from the point on the path closest to the searchlight?

## Homework Equations

[tex]\frac{dx}{dt}[/tex] = 5km/h

[tex]\frac{d\theta}{dt}[/tex] = ?

## The Attempt at a Solution

Reading the question, it is obvious that the situation above describes a right triangle:

I need to find the rate of change of [tex]\theta[/tex] with respect to x, or time. The rate of change of x with respect to time is 5km/h. First I believe I need to relate [tex]\theta[/tex] with x (time). This is probably obvious, but I'm not sure how to do it. I think I need to set up theta as a function of x as follows:

[tex]\theta[/tex] = tan[tex]_{-1}[/tex][tex]\frac{20}{30}[/tex]

Thus,

[tex]\theta[/tex] = tan[tex]_{-1}[/tex][tex]\frac{x}{30}[/tex]