Answer:
10.8 feet
Step-by-step explanation:
You want the length of the shadow of a 27 ft tree if a 5 ft post casts a 2 ft shadow.
The shadow length is proportional to the object height, so you have ...
(tree shadow)/(tree height) = (post shadow)/(post height)
x/(27 ft) = (2 ft)/(5 ft)
x = (27 ft)(2/5) = 10.8 ft
The length of the tree's shadow is 10.8 feet.
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To decide the length of the tree's shadow, we can utilize the idea of comparable triangles. Length of the Tree = 10.8 feet..
Since the wall post and the tree are both creating shaded areas simultaneously, we can set up an proportion between their heights and the lengths of their shadows.
We should indicate the length of the tree's shadow as x. We have the following proportion: (height of tree)/(length of tree's shadow) = (height of wall post)/(length of wall post's shadow).
Substituting the given qualities, we have: 27 ft/x = 5 ft/2 ft.
We can cross-multiply to solve for x: 27 ft * 2 ft = 5 ft * x.
Working on the equation gives us: 54 ft = 5 ft * x.
Simplifying the two sides by 5 ft provides us with the length of the tree's shadow: x = 54 ft/5 ft , x = 10.8 feet.
Calculating the expression offers us the last response, which is the length of the tree's shadow in feet.
To learn more about Numerical Problems,
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