a tree casts a shadow that measures 5m. At the same time a meter stick casts a shadow that is .4 m long. how

Question

I know that a meter is 3.28feet so do I multiply 3.28ft by .4m and divide by 5m to get the length.

Answer 1

You don't have to switch units... do everything in meters.

Similar triangles:

|
|
|
| x
|
|__5__

|
| 1
|
|_0.4_

Let x = tree height in meters

x ... 5
-- = ---
1 .. 0.4

x = 5 / (4/10)
x = 5 * (10/4)
x = 50/4
x = 12.5 m

The tree is 12.5 m tall

As a double-check think about your answer. The 1 meter stick casts a shadow that is shorter (0.4 as long)

The tree (12.5m) casts a shadow that is 0.4 as long.
12.5 * 0.4 = 5m

If you do want the answer in feet, you would just multiply this answer 12.5m x 3.28 ft/m = 41 ft.

Answer 2

Don't convert to feet. Stay in meters. You have two ratios:
(1/.4) = x/5 [this is the actual length of each object over the shadow length of each object...x is the height of the tree]. So you get the crossproduct of .4x = 5. So x = 25/2 = 12.5 meters.

Answer 3

why do you convert from meters to feet when all the units are in meters.

In the given problem the only unknown thing is tree's height.

frame the ratio

tree height/meter stick height = tree shadow/ stick shadow

tree height = h m

meter stick height = 1 m

length of tree shadow = 5m

length of meterstick shadow = 0.4 m

h/1 = 5/0.4

h = 5/0.4 = 50/4 = 12.5 meters

so the height of tree is 12.5 meters

Answer 4

Set up a ratio Ht/St = Hm/Sm
where:
Sm is shadow of meter stick .4m
Hm is height of meter stick 1m
St is shadow of tree 5m
Ht is height of tree

Ht/St = Hm/Sm
Ht/5m = 1/.4 Multiply both sides by 5m
Ht = (1/.4) (5)
Ht = 12.5