Friday, 13 March 2009

Right-Angled Triangles

Right-angled triangles are very convenient for mathematicans because they can give us so much information. You may think that this is a bit artificial because you don't see right-angles in nature. Well they are really common. If you want to know the height of something then that is handy because heights are vertical and the ground is horizontal. You don't need to climb a tree to know it's height. All you have to do is measure a distance from the tree and know the angle to the top of the tree. So now you know that right-angles are important, how do you deal with them?

The longest side of the right-angled triangle is called the 'hyp0tenuse'. Pick one of the angles (not the right-angle) and the side next to it is called the 'adjacent'. The side opposite this angle is called the 'opposite'.

The three basic ratios that you need to know with these triangles are the sine, cosine and tangent ratios. The tangent is useful if you want to know the height of the tree because you can measure the angle between the ground and the distance to the tree and all you need to know is a formula. The distance times the tangent of the angle equals the height. You can just accept this but I will explain it in later blogs.

That sums it up.

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