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Right Triangles and Trigonometry Videos 37 videos
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...
Mosquitos need their caffeine, just like the rest of us. Wouldn't think zipping around and stinging people all day long sap your energy?
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 1812 Views
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Description:
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 porridge included.
Transcript
- 00:00
Sines, a la Shmoop. Darren is the daredevil of the alligator world.
- 00:13
Slithering into the water at ground level isn’t enough of a rush for him.
- 00:18
So he has decided to dive in from a height of 10 feet.
- 00:22
This should certainly get him a mention on the Nightly Lizard News.
- 00:31
To accomplish the feat, he’ll be leaping off the roof of Crazy Cajun’s Crab Shack.
Full Transcript
- 00:37
However, he wants to make sure the height is really at least 10 feet. How can he be
- 00:43
certain? We can label our variable, the height of the
- 00:46
building, h.
- 00:48
Darren knows that the ladder he used to get up to the roof is 12 feet long…
- 00:53
…and the angle of elevation, or the angle between the ladder and the ground as he puts
- 00:57
the ladder against the shack…
- 01:00
…is 55 degrees. We know the length of the hypotenuse of the
- 01:03
triangle and the angle.
- 01:05
We want to find the length of the opposite side to the angle, so we can use the sine
- 01:11
function to help us.
- 01:12
The sine function tells us that the ratio is the opposite side of the triangle over
- 01:17
the hypotenuse.
- 01:19
Plugging in what we know, sine of 55 degrees equals h, the opposite side, over 12, the
- 01:25
hypotenuse.
- 01:26
To isolate h, we can multiply both sides by twelve…
- 01:30
…and we find that h equals twelve times the sine of 55 degrees, or approximately 9.83
- 01:39
feet. Looks like the Crab Shack isn't quite 10 feet
- 01:44
high. Darn.
- 01:45
Darren decides to check out the sines of other angles of elevation.
- 01:49
Maybe he can find a slightly taller shack nearby that will be better suited for his
- 01:55
record-breaking attempt.
- 01:57
He picks a few special angles for sine and tests them out:
- 02:01
Zero degrees, thirty degrees, forty-five degrees, and sixty degrees.
- 02:05
Doing some calculations, we find that:
- 02:08
The sine of zero degrees is 0.
- 02:10
The sine of thirty degrees is ?, or 0.5.
- 02:14
The sine of 45 degrees is one over the square root of two, or .707.
- 02:22
The sine of 60 degrees is the square root of three over two, or .866.
- 02:27
12 times .866 is greater than 10…
- 02:31
…so once Darren can find a building at the water’s edge where his ladder creates a
- 02:36
60 degree angle to the top of the roof…
- 02:39
…he’ll be all set! Now all he has to worry about is getting a
- 02:43
bad mark from the Russian judge.
- 02:46
That guy is a notorious gator hater.
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