SOLUTION: 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. Dete

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)
Found 3 solutions by MathLover1, MathTherapy, greenestamps:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

Consider the post and its shadow as a right angled triangle.
The post is the opposite side, the shadow is the adjacent side.
Using trigonometric ratios:

Note is

degrees.
Now consider the building.
The building is the opposite side, and its shadow is the adjacent side.
since is , we have

->This is the height of the building.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
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)

The height of the building, and its shadow are proportionate to the height of the post and its shadow.
This results in:

Let the building's height be H
We don't have to change the units, so we keep them in FEET
The above becomes:
------Cross-multiplying
Height of building, or
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 .
FYI: 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.
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

As the second tutor said, your method was fine except that you didn't use compatible units.

Your formal method uses a proportion, saying that the ratio of the building's height to the length of its shadow is the same as the ratio of the post's height to the length of its shadow. You just overlooked the fact that for the post the given information had the height in feet and the length of the shadow in inches.

I would encourage you not to be a slave to the formal process of setting up and solving a proportion. In fact, the mistake you made was probably because you just looked at the numbers and set up the proportion, without paying attention.

Instead, think about the actual physical problem; you will be less likely to make the kind of mistake you made. You have a post that is 3 feet tall and casts a shadow 4 inches long. 3 feet is 36 inches; 36 inches is 9 times 4 inches; so the height of the post is 9 times the length of its shadow.

But that means the height of the building will be 9 times the length of its shadow. 9 times 90 feet is 810 feet.
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