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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
Full Transcript
- 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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