In a rugby game, a try is scored 15 m from the left-hand goal-post. The conversion kick is
taken at some point on the line perpendicular to the goal-line from the point where the try was
scored, as shown in the diagram below.
The ball needs to pass between the goal-posts, which are 5.4 m apart.
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Find the distance d from the goal-line that the conversion kick should be taken from in order
to maximise the angle θ between the lines from the ball to the goal-posts.
*You must use calculus and show any derivatives that you need to find when solving this
problem.*
*You do not need to prove that the angle you have found is a maximum.*