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The Tangent Function 1565 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.

Language:
English Language

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.

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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