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Law of Sines 1895 Views


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Description:

The law of sines is all about proportions, so make sure to keep yours in order.

Language:
English Language

Transcript

00:03

Law of Sines, a la Shmoop. Dr. Dorito is entering airport security at

00:10

Square Island He looks a little different from all the other

00:14

square inhabitants, so Square Island security is a bit wary of him.

00:18

His less-than-90 degree angles and weirdly slanted arms are also a bit suspicious.

00:24

They want to figure out all his side lengths and angles before letting him through.

00:31

Dr. Dorito tells security that two of his lengths are 3.2 and 4, and that his angle

00:38

A is 60 degrees. Given Angle-Side-Side, to figure out the rest

00:44

of the angles and side lengths, they'll use the law of sines.

00:50

Sine A over a equals sine B over b.

00:55

We can plug in A as 60 degrees, and side length A as 4.

01:00

The only other side we have is 3.2, so that'll be b.

01:05

We have sine of 60 degrees over 4 equals sine of the angle at point B over 3.2, the side

01:12

length of b. To solve for angle B, we can multiply both

01:16

sides by 3.2. We want B, not sine B. So if we take the inverse sine of each side, we

01:31

see that B is around 43.9 degrees. Wonderful. Now we have two out of three angles

01:38

and two out of three sides. Knowing that all the angles in a triangle

01:43

add up to 180° allows us to find the last angle.

01:48

Substitute in the angles we know. A as 60 degrees and B as 43.9 degrees.

01:55

To solve for C, we can subtract 60 and 43.9 from both sides, to get C equals 180 degrees

02:04

minus 60 degrees plus 43.9 degrees... ...to get that C equals 76.1 degrees.

02:13

One side to go. We can use either the ratio between sine 60 degrees and 4 or sine 43.9

02:20

degrees and 3.2. Let's use the ratio between sine 60 degrees

02:25

and 4. Substitute what we know. We're looking for

02:29

the last side, c. To solve for side length c, we can rearrange

02:34

the equation by cross-multiplying. Sine sixty degrees times c equals 4 times

02:40

sine 76.1 degrees. To isolate c, we can divide both sides by sine sixty degrees...to get

02:53

that c equals around 4.5. Double-checkin' time. Do we know all of Dr.

03:00

Dorito's angles and all the sides? Yup, sure do. All three side lengths and all

03:05

three angles. Now they just have to make sure he's not smuggling

03:09

any zesty taco flavoring across the border...

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