Asked by Alexa
A statue 10 feet high is standing on a base 13 feet high. If an observer's eye is 5 feet above the ground, how far should he stand from the base in order that the angle between his lines of sight to the top and bottom of the statue be a maximum?
Answers
Answered by
Steve
If the angles to the bottom and top are a and b, then from a distance x we have
tan(a) = 8/x
tan(b) = 18/x
We want the angle c=b-a, so
c = arctan(18/x)-arctan(8/x)
dc/dx = 10(144-x^2)/((x^2+8^2)(x^2+18^2))
dc/dx=0 at x=12
tan(a) = 8/x
tan(b) = 18/x
We want the angle c=b-a, so
c = arctan(18/x)-arctan(8/x)
dc/dx = 10(144-x^2)/((x^2+8^2)(x^2+18^2))
dc/dx=0 at x=12
Answered by
Alexa
Sorry for asking, but why did tan(a) become 8/x and tan(b) 18/x?
Answered by
Steve
because that's the definition of tan(a): opposite/adjacent.
Did you draw a diagram of the setup? That's the first step to all of these problems.
Did you draw a diagram of the setup? That's the first step to all of these problems.
Answered by
Alexa
Thank you so much
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