When I started looking at right-angled triangles I said they may not be rare in nature because you have horizontal ground and lots of things like trees that are vertical. If you want to know the height of a cliff then you don't need to climb it with a tape measure. What happens if you fold a square or a rectangle diagonally? You end up with two right-angled triangles. What happens if you lean a ladder against a wall. This is an obvious right-angle because the ladder is the hypotenuse.

Let's look at the sine of an angle. You have to start with an angle in a right-angled triangle that is not the right-angle. Take the angle between the ladder and the floor, and let's call it x degrees. The sine of this angle is the opposite divided by the hypotenuse. In an abbreviated form you get sin x = opp / hyp. Just take the first letters S=O/H. Similarly the cosine is the adjacent divided by the hypotenuse C = A/H. Finally the tangent is the opposite divided by the adjacent. T=O/A.

Miss out the division sign (but don't forget about it) and the way to remember what the sine, cosine and tangent do is SOH, CAH, TOA.

That sums it up.

## Sunday, 15 March 2009

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