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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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