You are running down the boundary line dribbling the ball in soccer or hockey. Investigate where in your run the angle the goal mouth makes with your position is at a maximum.

Yogendra

Hi Yogendra,

I added some labels to the diagram you sent.

Let p be the measure of the angle CAB and q be the measure of the angle DAB, both in radians. Then using the diagram and some algebraic simplification I get

Theta is a function of x so you can differentiate both sides with respect to x and find the value of x where the derivative of theta with respect to x is zero.

Penny

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