Question 1190310
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The answer from the first tutor uses algebra and equations of lines to solve the problem.  That is a valid approach (and you should understand and be able to use it), but it is not very efficient.<br>
The response from the other tutor gives you the right answer; but you learn nothing from it.<br>
If you run into this kind of problem frequently -- e.g., if you compete in timed math competitions -- then this is a handy formula to memorize:<br>
If the heights of the two towers are A and B, then the height where the wires cross is {{{AB/(A+B)}}} -- independent of the distance between the towers.<br>
If you want to LEARN something about that formula, you can derive it using similar triangles.<br>
Here is a diagram....<br>
{{{drawing(400,400,-2,12,-2,16
,line(0,0,10,0),line(0,0,0,8),line(10,0,10,12),line(0,8,10,0),line(0,0,10,12)
,line(4,0,4,4.8)
,locate(-1,-.5,"A(0,0)"),locate(9,-.5,"C(10,0)"),locate(-1,9,"B(0,8)"),locate(9,13,"D(10,12)"),locate (4,6,E),locate(4,-.5,F)
,locate(2,1,x),locate(6,1,"10-x"),locate(4.5,2.4,y)
,locate(.5,4,8),locate(9,6,12)
)}}}<br>
(1) Triangles CEF and CBA are similar:<br>
{{{EF/AB=y/8=(10-x)/10}}}<br>
(2) Triangles AEF and ADC are similar:<br>
{{{EF/CD=y/12=x/10}}}<br>
From (1) and (2),<br>
{{{y/8+y/12=(10-x)/10+x/10=10/10=1}}}<br>
Solve for y:<br>
{{{y/8+y/12=1}}}<br>
Multiply by the common denominator, without simplifying:<br>
{{{12y+8y=12*8}}}
{{{y(12+8)=12*8}}}
{{{y=(12*8)/(12+8)}}}<br>