How can I find an answer to this math prob.?

Question

Amy who is 5 ft tall casts a 4 ft shadow when a pine tree has an 8 ft shadow. How tall is the pine tree? and how do I do the math of it? Thanks

Answer 1

I'm not quite sure about this, but I think it has something to do with enlargement.

let I/O , where I is the image and O is the object.

Since they have the same light source (that is the sun, I assume)
, therefore

I/O = 4/5 = 8/p

4p = 5*8 = 40

therefore p = 10 , which is the height of the "real" pine tree.

I'm could be wrong, so you should see other people's answer, which might give you more detail.

Answer 2

It's basically proportions. Here is how to do it:
5/4=x/8
You have the height of each object over the shadow length.
Then you do cross multiplying, so 5 time 8 and 4 times x.
Since 5 times 8 is 40, then 4 times x is equal to 40.
You then do 40 divided by 4 to get x:
40 divided by 4 is 10
SO, the pine tree is 10 feet tall.
I hope this helped! I did this in my seventh grade math class, I'm glad I remembered it!

Answer 3

For this problem, you have 2 similar right triangles created, one from the pine tree and its shadow, the other from Amy and her shadow. For both triangles, we do not know the hypotenuse for either one, but we do know the 2 sides for each:

The Amy triangle has height of 5, and length of 4. The pine tree triangle has an unknown height, which we will call H for now, and length of 8. These are similar triangles because they have the same values for their angles, even though their sides are of different lengths. How do I know this? Because both shadows are being created from the same source - the sun. When this happens, the angles involved are congruent for each respective triangle.

With similar triangles, you have a special property which says the sides of each respective triangle have the same ratio. What this means is 5/4 = H/8. Now you can solve for H. :)

Answer 4

Use a proportion ratio:

Actual height
_____________
Shadow length

5ft ?
____ = _________
4ft 8 ft


Cross-multiply

5 times 8 = 4 times ?
40 ft = 4 times ?

Divide by 4

10 ft = ?

The pine tree is 10 feet tall

Answer 5

By using ratios.

height/shadow is same for both so,
5ft/4ft= T/8ft , where T is how tall pine is.
You multiply both sides with 8, to get it away from right side.

5*8ft
---- = T =
4ft

40ft
--- = 10ft = how tall pine is
4ft

(you can also get formula that you can use later on if you remember that:

from
a . . x
-- = -- you can get anyone of these a,b,x,y if you know all others.
b . . y

if you want a or x you just multiply with the denominator of that variable that you want to know. So

2 . . x . . . . . . . 2*6 . . x*(6)
-- = --- . is . . . ---- = -------- and you can take(6) out
3 . . 6 . . . . . . . . 3 . . . . (6)

and you have
2*6
---- =12/3 = 4 = x
3

so for a/b = x/y
x is allways

a*y
-----
b

, and if you need b or y just flip both sides up side down (to b/a=y/x) and do as above.

if you forget these, you can always try these out with small numbers on some corner of your test paper.)

p.s. dots ( . ) are just for space ignore them.

Answer 6

you have to set up proportion.
5 ft is to 4 ft as x is to 8ft.
you're solving for the x .
now cross multiply and solve for x alegebraicly.

the pine tree is equal to 10 ft when you solve it .

Answer 7

5/4=x/8. Crossmultiply, and 40=4x. 10=x.

Answer 8

Your substantial aim is to place the x's on one area, and the numbers on the different area. SO: -4x + 8 = -2x +12 (circulate the -4x to the different area of the equivalent, remembering to alter its sign): 8 = 2x + 12 (Now circulate the 12 to the different area of the equivalent, additionally remembering to alter its sign): -4 = 2x (Now you attempt to get rid of something caught to the x, so to that end divide by utilizing 2): x = -2 And it rather is the respond! i'm hoping you acquire it!

Answer 9

these are simply raioes
5/4=x/8
40=4x
x=10

Answer 10

Ratios.