Help with a math word problem?????

Question

I know the answer to the following problem is 54 feet I just don't know why that is. Please help!

1. The length of the shadow of a flagpole was found to be 72 feet. The shadow of a 3 foot picket fence in line with the flagpole was 4 feet. What is the height of the flagpole.

Answer 1

Hi,

Just set up a proportion:

height of fence......height of flagpole
---------------------.=.------------------------
fence shadow........flagpole shadow

3........x
----.=.----
4........72

Now cross multiply and solve!

4x = 3(72)
4x = 216
x = 54

I hope that helps!! :-)

Answer 2

An object that's sticking out perpendicular to the ground is going to make a right angle with its shadow, which means the base of the object, top of the object, and the tip of the shadow make a right triangle. If we think of there being two different right triangles here, then the angle at the tip of each shadow is going to be the same (because the sun is still at the same point in the sky).

Call this angle θ. Then with the fence shadow, tan(θ) = 3/4. With the flagpole, tan(θ) = h/72 where h is the flagpole's height. This means 3/4 = h/72, which you can solve for h.

Answer 3

Look at it like a fraction:

shadow of fence/height of fence = shadow of flag pole/height of flag pole

where as:

3/4 = 72/x

Solve for x:
x =54

Answer 4

Let the height be y

3 will produce 4 feet that means y will produce72

3=4
y=72

cross multiply the two equations

3x72=4xy

216=4y


y=54.

Answer 5

here you go

you take the 2 factors given of the fence

3/4 = length of pole/ length of shadow = x/72
3/4=x/72
3/4*72=x
54=x

yeah something like that

Answer 6

Proportional Problem

3/4 = x/72

4x = 3(72)

4x = 216

4x / 4 = 216 / 4

x = 216/4

x = 54

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