<PRE><B>Question 1025720</B>
your diagram looks like this as far as i can tell.


&lt;img src = &quot;http://theo.x10hosting.com/2016/031902.jpg&quot; alt=&quot;$$$&quot; &lt;/&gt;


from this diagram, you get:


tan(35) = x/y


tan(7) = (14-x)/y


solve for y to get:


y = x/tan(35) and y = (14-x)/tan(7)


this results in x/tan(35) = (14-x)/tan(7)


multiply both sides of this equation by tan(7) * tan(35) to get:


x*tan(7) = (14-x)*tan(35)


simplify to get:


x*tan(7) = 14*tan(35) - x*tan(35)


add x*tan(35) to both sides of this equation to get:


x*tan(7) + x*tan(35) = 14*tan(35)


factor out the x to get:


x*(tan(7) + tan(35)) = 14*tan(35)


divide both sides of this equation by (tan(7) + tan(35)) to get:


x = (14*tan(35)) / (tan(7) + tan(35)


solve for x to get:


x = 11.91129969


14-x is therefore equal to 14 - 11.91129969 = 2.08870031


y = x/tan(35) results in y = 11.91129969/tan(35) which results in y = 17.01109891


y = (14-x)/tan(7) results in y = 2.08870031/tan(7) which results in y = 17.01109891.


value of y looks good either way.


looking at the diagram, we see that:


BC = x = 11.91129969


CD = 14 - x = 2.08870031


BD = the height of the flagpole = BC + CD = 14.


y = AC = the distance between the woman and the flagpole = 17.01109891.


AE = distance between the height of the woman and the ground = 14 - x = 2.08870031.


since the height of the woman is 1.73, then the hill she is standing on must be 2.08870031 - 1.73 = .3587003101.


looks like we have everything you need.


her distance to the flagpole is 17.01109891 meters.


the height of the hill is .3587003101 meters.


i double checked my results and i believe they are correct.


hopefully you agree after looking at what i did.






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