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?

Answer 1

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

Answer 2

Sorry for asking, but why did tan(a) become 8/x and tan(b) 18/x?

Answer 3

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.

Answer 4

Thank you so much