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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.
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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