# Sines

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Geometry | Right Triangles and Trigonometry |

Language | English Language |

Right Triangles and Trigonometry | Law of Sines and Law of Cosines |

### Transcript

However, he wants to make sure the height is really at least 10 feet. How can he be

certain? We can label our variable, the height of the

building, h.

Darren knows that the ladder he used to get up to the roof is 12 feet long…

…and the angle of elevation, or the angle between the ladder and the ground as he puts

the ladder against the shack…

…is 55 degrees. We know the length of the hypotenuse of the

triangle and the angle.

We want to find the length of the opposite side to the angle, so we can use the sine

function to help us.

The sine function tells us that the ratio is the opposite side of the triangle over

the hypotenuse.

Plugging in what we know, sine of 55 degrees equals h, the opposite side, over 12, the

hypotenuse.

To isolate h, we can multiply both sides by twelve…

…and we find that h equals twelve times the sine of 55 degrees, or approximately 9.83

feet. Looks like the Crab Shack isn't quite 10 feet

high. Darn.

Darren decides to check out the sines of other angles of elevation.

Maybe he can find a slightly taller shack nearby that will be better suited for his

record-breaking attempt.

He picks a few special angles for sine and tests them out:

Zero degrees, thirty degrees, forty-five degrees, and sixty degrees.

Doing some calculations, we find that:

The sine of zero degrees is 0.

The sine of thirty degrees is ?, or 0.5.

The sine of 45 degrees is one over the square root of two, or .707.

The sine of 60 degrees is the square root of three over two, or .866.

12 times .866 is greater than 10…

…so once Darren can find a building at the water’s edge where his ladder creates a

60 degree angle to the top of the roof…

…he’ll be all set! Now all he has to worry about is getting a

bad mark from the Russian judge.

That guy is a notorious gator hater.