ShmoopTube

Where Monty Python meets your 10th grade teacher.

Search Thousands of Shmoop Videos

Law of Cosines 1130 Views


Share It!


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.

Language:
English Language

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…

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.

Up Next

Verifying Trig Identities
1729 Views

Verifying trig identities is important, especially when you're about to let one of them into the country—which is why they should keep their pass...

Related Videos

Tangent Half-Angle Formula
1361 Views

Mosquitos need their caffeine, just like the rest of us. Wouldn't think zipping around and stinging people all day long sap your energy?

SOHCAHTOA
4605 Views

Sine is the opposite over the hypotenuse; cosine is the adjacent over the hypotenuse; and tangent is the opposite side over the adjacent side....

Sines
1811 Views

Shmoop saw the sine. Want to pull an Oliver Twist and ask us for more? We've gotcha covered. Head over to /video/math/ for more mathy goodness. No...

Cosines
1273 Views

It's the sine! No, it's the tangent! No, it's the cosine! Alright, so maybe evaluating trigonometric functions isn't as exciting as spotting Superm...