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maximum value of theta angle

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A missile is launched and travels along a path that can be represented by:

A radar tracking station is located 2 km directly behind the launch pad. Placing the launch pad at the origin and the radar station at (-2, 0), find the largest angle of elevation required of the radar to track the missile.
I included the equation in the attachment
Please show work.

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The maximum value of theta angle is explored.

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At any moment, the height of the missle is y while the horizontal distance between the missle and the station is ...

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