# Help for solving this optimisation problem please

Hi, I’m a bit confused on this question because when I look at the triangle it does not look like a right angled triangle. So I’m finding it kind of hard to come up with a formula that will allow me to maximise the angle, in the question.
I would really appreciate it if I could get some help on how to solve this question.
Thank you!!

You are right, @Faadhilah the triangle is not right angle triangle but we can add some lines to the diagram to make one (or two!):

Now we have two right angle triangles which share side x:

• one with the sides x and 354.2m (328 + 26.2) and an angle B

• another with the sides x and 26.2m and an angle A

The angle theta which we need to maximize is equal to (B - A) so we can find:

In the interval 0 to 90 the maximum value of an angle will give us the maximum value of tan of this angle.
If

then

Solving this equation we will have x = 96.33m which will make the angle theta equal to 59.6 degrees. However, this spot is not in the park so Mark has to choose the closest end of the park (x = 500m) which would give him a viewing angle of 32.3.

Intuitively, it is obvious, but why not have some fun nd use differentiation to prove it?

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