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Law of Cosines 1130 Views
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Description:
The law of cosines allows you to find angle measurements if you have the side lengths. You know, in case you run into that situation on Saturday night.
Transcript
- 00:04
Law of Cosines, a la Shmoop. Anthony, Bernardo and Chuckles, three members
- 00:09
of the mafia…
- 00:10
…were all contracted to whack one another.
- 00:15
They all ended up in the same place at the same time, and next thing they knew, they
- 00:19
were trapped in a standoff. There is 45 feet between Anthony and Bernardo…
Full Transcript
- 00:26
…74 feet between Bernardo and Chuckles…
- 00:30
…and 61 feet between Chuckles and Anthony.
- 00:34
What are the angles between each? If we picture the scenario as a triangle,
- 00:40
the side are 45, 74 and 61.
- 00:45
Given three sides of the triangle, we’ll need to figure out the angles with the law
- 00:50
of cosines. The Law of Cosines tells us that a squared
- 00:54
equals b squared plus c squared minus 2 b times c times cosine of the angle A.
- 01:03
Before we plug in all the values we know, let’s isolate what we’re solving for:
- 01:09
the angle A. Subtract a squared and add 2bc cosine A to
- 01:15
both sides of the equation to get 2bc cosine A equals b squared plus c squared minus a
- 01:23
squared. Then divide both sides by 2bc to get cos A
- 01:28
equals b squared plus c squared minus a squared all over 2bc.
- 01:34
To isolate the angle, we can take the cosine inverse of both sides, and when we do, we
- 01:39
end up with the angle A equals the cosine inverse of b squared plus c squared minus
- 01:45
a squared all over 2bc. Now let’s plug in b as 61, c as 45, and
- 01:52
a as 74. Plugging it into our calculators, we see that
- 01:56
angle A equals around 87.2 degrees. To find angle B, we can use the Law of Cosines
- 02:33
again…and we find that b equals around 55.4 degrees.
- 02:54
We know that all the angles in a triangle total 180 degrees…
- 02:57
…so we can just take 180 degrees minus 87.2 minus 55.4 to find angle C…
- 03:05
…which gives us 37.4 degrees. However, it’s going to take more than a
- 03:10
basic understanding of cosines to get Anthony, Bernardo and Chuckles out of their pickle.
- 03:14
They might be here a while. Good thing somebody
- 03:29
ordered pizza.
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