Question 127043: A 10-foot pole casts a shadow of 5 feet. How tall is a tree with a shadow of 13 feet? Not sure how to get that. Please help Found 2 solutions by stanbon, Earlsdon:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! A 10-foot pole casts a shadow of 5 feet. How tall is a tree with a shadow of 13 feet? Not sure how to get that.
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object/shadow = object/shadow
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tree/13' = 10'/5'
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tree = 13(10/5)
tree = 13(2)
tree = 26 feet
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Cheers,
Stan H.
You can put this solution on YOUR website! You can solve this kind of problem using the principle of similar triangles.
In similar triangles, corresponding sides are proportional.
What are the triangles in your problem? There are two right triangles.
One of them is formed by the tree and its shadow where the tree is represented by the height of the triangle and the shadow is represented by the base of the triangle. The hypotenuse is the line connecting the top of the tree to the end of its shadow.
The other right right triangle is formed by the 10-foot pole (the height) and its 5-foot shadow (the base).
Now we compare the bases of the two triangles (these are corresponding sides) and note that they are proportional because the two triangles are similar, so we can wite:
(13-foot shadow of the tree)/(5-shadow of the pole) This is one part of the proporion.
The other part is formed by the (height (h) of the tree)/(the 10-foot pole)
Putting it all together, we have: Multiply both sides by 10. Simplify.
The height of the tree is 26 feet.
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