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SVEN [57.7K]
4 years ago
8

A tree casts a shadow 28 feet long. At the same time. A 5ft tall boy casts a shadow 8ft long how tall is the tree?

Mathematics
1 answer:
OlgaM077 [116]4 years ago
5 0

Answer:

The tree is 17.5 ft tall

Step-by-step explanation:

We can use ratios to solve

Shadow

-----------

height

28          8

------ = ------------

tree         5

Using cross products

28*5 = 8 * tree

140 = 8 * tree

divide each side by 8

140/8 = 8 *tree/ 8

17.5 = tree

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the length of AC can be calculated with the theorem of Pythagoras:

length AB = a - 0 = a
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seeing as the length of AC is the longest, it can be calculated by the following formula:

It is called "Pythagoras' Theorem" and can be written in one short equation:

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in this case, A and B are lengths AB and BC, so lenght AC can be calculated as the following:

a^2 + b^2 = (length AC)^2
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Extra information: Seeing as the shape of the drawn lines is a rectangle, lines AC and BD have to be the same length, so BD is also √(a^2 + b^2). But that is also stated in the assignment!


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