Law of Sines?

A friend of mine made this picture to illustrate the law of sines.
http://img27.photobucket.com/albums/...w_of_sines.jpg

I kinda see a pattern, but not completely...and I don't know how this knowledge would be useful.

It's not really. Sure, it shows what is going on, but I don't think I'd put that in a tutorial or anything.

Quote:

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and I don't know how this knowledge would be useful.

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law of sines can be used to find the length of a side, given you know one other side's length and angle opposite to it, and know the angle of the side opposite to it(you probably gathered this). The uses are numerous, and include triangulation of an object(such as the moon).

the theorem stateshttp://hyperphysics.phy-astr.gsu.edu...mages/lsin.gif

what the hell is the point of this thread?? and, yes law of sines and cosines is very useful...how can you not see that?? ahhhhh




;)

Here's a sample application:

You're in engineering, and need to know the height of an object. You're standing 50 meters away from the base of the object, and when you measure from the ground to the top of the object, it is a 48 degree angle (from horizontal). You know that the object makes a 83 degree angle with the ground.

Hint: Draw a diagram to understand it better. I can't make up one right now.

Solution:

Code:

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let d be the distance from you to the object
let h be the height of the object
let theta be the angle from the ground to the top
let alpha be the angle the object makes with the ground
let gamma be the other angle in the triangle

gamma = 180 - theta - alpha
      = 49

sin gamma / d = sin theta / h
sin49 / 50    = sin48 / h
h            = 50sin48 / sin49
h            = 49.23 (approx)

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Here's a diagram.

What's it useful for? It's useful so we can algebraically find values of sides and angles of trianges we wouldn't otherwise be able to find, without measuring ourself.