Let's take a common sense approach looking at right angle triangles and how trigonometry is used. Every book you learned from probably dealt with terms like side adjacent, side opposite, etc. etc... Well I am going to use easy terms like longer leg, larger angle and so on. Sorry you will still have to know what the hypotenuse is. Remember that it is the longest side of a right angle triangle.
NOTICE   THESE   THINGS : The term larger angle means larger than the smaller not larger than the 90 degree angle. The 90 degree angle is always the largest angle of the three. The larger angle and the smaller angle added together always equal 90 degrees. The Legs (Shorter and Longer) are always next to the 90 degree angle. The Hypotenuse is on the opposite side of the 90 degree angle and next to the smaller and larger angle. Notice how the shorter leg is opposite the smaller angle (Makes sense doesn't it?), and the longer leg is opposite the larger angle . One more thing, if the smaller or the larger angle is equal to 45 degrees then we cannot call them larger or smaller because they will be the same size. We will have an isosceles right angle triangle. No wonder the tangent of 45 degrees is equal to one (the legs will be a one to one ratio to each other).
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