Question 1203323
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Answer: <font color=red size=4>703.609 feet</font> (approximate)



Explanation


Let's start off with a rough sketch of the diagram
*[illustration Screenshot_243.png]
The key points are
A = base of the building
B = location of the person's eye
C = base of the monument
D = location on monument at the same height level as the person's eye
E = top of the monument


We have these variables
x = distance from B to D = distance from A to C
y = distance from C to D


Note how segment DE is 200-y feet long so that CE = CD+DE = y + (200-y) = 200


Let's focus on triangle BCD.
tan(angle) = opposite/adjacent
tan(angle DBC) = CD/BD
tan(2) = y/x
y = x*tan(2)
This will be used later in a <font color=blue>substitution</font> step.


Now focus on triangle DEB.
tan(angle) = opposite/adjacent
tan(angle DBE) = DE/BD
tan(14) = (200-y)/x
tan(14) = (200-<font color=blue>x*tan(2)</font>)/x ........ <font color=blue>substitution</font>
x*tan(14) = 200-x*tan(2)
x*tan(14)+x*tan(2) = 200
x*( tan(14)+tan(2) ) = 200
x = 200/( tan(14)+tan(2) )
x = 703.609019511759 approximately
x = <font color=red>703.609</font>


Make sure your calculator is in degree mode.
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