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Tangents and Secants Videos 5 videos
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The Tangent Function 1571 Views
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Description:
Ever had someone tell you that getting pooped on by a bird was good luck? Yeah, we never fell for that one either. Watch this video to see how math can help you avoid those stinky bird bombs.
Transcript
- 00:04
The Tangent Function, a la Shmoop.
- 00:07
Archduke James XIV is a tanned gentleman who enjoys spending his days on the beach.
- 00:13
Unfortunately, James has an overwhelming fear of being the victim of seagull air raids.
- 00:19
He figures that as long as he can calculate how high the seagulls are flying,
- 00:24
he can get out of the way in time.
Full Transcript
- 00:26
How high are the seagulls flying?
- 00:29
We can define the height of the seagulls with the variable h.
- 00:32
We also know that James is sunbathing exactly 42 feet away from the shoreline.
- 00:37
Luckily, James has always aspired to be a sailor, so he happens to have his handy-dandy
- 00:42
sextant, which he can use to tell the angle between two things.
- 00:47
His sextant tells him the angle of elevation,
- 00:50
or the angle between the ground and the seagull, is exactly 51 degrees.
- 00:55
Because we know this is a right triangle with a 90 degree angle, we can use trigonometry
- 01:01
to help James find h, the height of the seagulls.
- 01:06
Let's use the tangent function, which tells us the ratio of the opposite side
- 01:10
to the adjacent side in a right triangle with a given angle.
- 01:15
So, using what we know, we can plug in the value of 51 degrees for the angle,
- 01:19
and 42 as the adjacent side.
- 01:22
We can plug in h as the opposite side, because it is "opposite" the angle.
- 01:27
To isolate h, we can multiply 42 to both sides,
- 01:33
to get h equals 42 times the tangent of 51 degrees...
- 01:39
…to get that the height equals about 52 feet.
- 01:42
Now that James knows how high the seagulls are flying, he doesn’t have to worry about
- 01:46
getting nailed by seagull bombs. But James is an adventurous soul, and wants
- 01:50
to be prepared for other beaches as well.
- 01:53
So he prepares some other handy tangent values
- 01:56
to calculate how high seagulls would be flying over neighboring beaches at other angles.
- 02:01
James decides to find the tangent values of a couple special angles:
- 02:05
zero degrees, thirty degrees, forty-five degrees, and sixty degrees.
- 02:11
Using his calculator, James finds that the tangent of zero degrees is zero…
- 02:16
…the tangent of thirty degrees is one over the square root of three, or .577…
- 02:23
…the tangent of 45 degrees is 1…
- 02:26
…and the tangent of 60 degrees is the square root of three, or 1.732.
- 02:32
James is finally ready to conquer any seagulls, at any beach, any time.
- 02:36
Now he just has to remember his sunscreen.
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