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Law of Sines and Law of Cosines Videos 5 videos
Sine is the opposite over the hypotenuse; cosine is the adjacent over the hypotenuse; and tangent is the opposite side over the adjacent side....
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...
The law of sines is all about proportions, so make sure to keep yours in order.
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.
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.
Full Transcript
- 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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