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Hi.
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In this video, we're given that we are a five -foot -tall person looking at a statue, which is on top of a base.
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The statue is 10 feet tall and the base is 13 feet.
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And the question is how far away should we stand in order to maximize the viewing angle? so the viewing angle i have labeled here as theta.
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And so you can sort of imagine in the extreme case, if you're very close, if you're very close to the statue.
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Your angle will be very small.
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Or if you're very far away, then your angle will be very small as well.
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So somewhere in between, we should have a maximum angle.
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So what we want to do, the overall steps of this problem are to come up with a function for theta given x.
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So x being the distance from the statute that we stand.
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And then we want to maximize that function.
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So the first step to find theta given x, what we have to do is we want to take this right triangle that i have drawn here, which indicates the viewing angle theta here.
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And then because this triangle, the viewing triangle is not a right triangle, we can't just solve for theta from there.
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So what we do is we solve for y and z.
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And then theta then is y minus c...