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TSI Math: Using Proportions to Find the Height of a Shadow
24 Views

Arya went for a walk in the woods and came upon a tree in an open field. The tree cast a 72-foot shadow. If Arya is five feet tall and cast a six-f...

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TSI Math: Using Proportions to Find the Height of a Shadow 24 Views


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Description:

Arya went for a walk in the woods and came upon a tree in an open field. The tree cast a 72-foot shadow. If Arya is five feet tall and cast a six-foot shadow, then how many feet tall is the tree?


Transcript

00:02

Okay sy math people We have a whole section here

00:05

on modeling A different kind of modeling area went for

00:10

a walk in the woods and came upon a tree

00:12

in an open field The tree cast a seventy two

00:15

foot shadow If area is five feet tall and cast

00:18

a six foot shadow Well then how many feet tall

00:21

is the tree Cool question All right well the treated

00:27

open field sounds picture ask very game of thrones e

00:30

now make a super unpick shirt a diagram of the

00:34

situation here aria and her shadow and the tree and

00:37

its shadow form two similar triangles like this The triangles

00:41

are similar because both aria and the tree stand perpendicular

00:44

to the ground and the sun shines on both of

00:47

them at the same angle right Similar triangles have proportional

00:50

sides right so let's let h stand for the height

00:53

of the tree instead of her proportion here So height

00:56

is to shadow as h is to seventy two as

00:59

five to six right are yet to tree and feet

01:02

cross multiply to solve and we've got six h is

01:05

seventy two times five or six h is three sixty

01:08

Divide both sides by six and we get that age

01:11

is sixty feet The height of the tree is sixty

01:14

feet so that's it The answer is being and four 00:01:17.295 --> [endTime] smoked along with aria

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