Question 1092255
You measure the shadow cast by a certain tall building and find that it is 90 feet long. Then you measure the shadow cast by a three-foot post and find it to be 4 inches long. Determine the building's height. 

I wrote it as x/90= 3/4 so 4x=90(3) but my answer was wrong. X= 67.5 (or 68)
<pre>The height of the building, and its shadow are proportionate to the height of the post and its shadow. 
This results in: {{{matrix(1,3, matrix(1,3, Height, of, building)/matrix(1,4, Length, of, "building's", shadow), "=", matrix(1,3, Height, of, post)/matrix(1,4, Length, of, "post's", shadow))}}}
   
Let the building's height be H 
We don't have to change the units, so we keep them in FEET 
The above becomes: {{{matrix(1,3, H/90, "=", 3/(4/12))}}}
{{{matrix(1,3, H * (4/12), "=", 3(90))}}} ------Cross-multiplying
Height of building, or {{{highlight_green(matrix(1,12, H, "=", 3(90)/(4/12), "=", 3(90), "*", 12/4, "=", 3(90) * 3, "=", 810, feet))}}}
Good try!! Everything you did was correct, with the exception that you made an error when you used 4 FEET for the shadow of the post, 
as opposed to {{{matrix(1,4, (4/12), of, a, foot)}}}.
<b>FYI:</b> You most certainly DO NOT NEED TO USE TRIG ratios to get the height. You already  know that anyway.
It's just that your setup had 4 feet instead of 4 inches.
IGNORE all that COMPLEX solution as it's TOTALLY, TOTALLY UNNECESSARY.