Sines

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GeometryRight Triangles and Trigonometry
LanguageEnglish Language
Right Triangles and TrigonometryLaw of Sines and Law of Cosines

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.