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The Angles of a Right TriangleHow do you calculate the angles of a right triangle? More importantly, how do you remember how to calculate them? Well, there is a trick, but first let's briefly talk about the sides of the triangle. We know that triangles have three sides. We also know that a right triangle contains one angle that is 90 degrees, that is, the legs that join at that angle are exactly perpendicular to each other. The three angles of the triangle add up to 180 degrees. To calculate one of the angles, you need to name the three sides of the triangle. The side that is directly across from the right angle and does not touch the right angle at either end, is known as the hypotenuse. The other two legs of the triangle are the adjacent and the opposite. Which is which depends on the angle you are trying to calculate. From that angle, the leg joining it that is not the hypotenuse, is the adjacent. The remaining leg, that is directly opposite the angle you are calculating, is the opposite. Now to calculate that angle, you need to know the lengths of those legs. Then you will use functions known as sine, cosine, and tangent. On your calculator they will be shown as SIN, COS, and TAN. Briefly, the sine of an angle is equal to the length of the opposite leg divided by the length of the hypotenuse (sin=opp/hyp). The cosine is equal to the length of the adjacent leg divided by the length of the hypotenuse (cos=adj/hyp). The tangent of an angle is equal to the length of the opposite leg divided by the length of the adjacent leg (tan=opp/adj). And now for the memory trick. Those three formulas can be summarized in the order mentioned above into one simple word: SOHCAHTOA (pronounced soak-a-toe-AH!). S stands for sine, O for opposite, H for hypotenuse, C for cosine, A for adjacent, and T for tangent. Remember that and you'll never be at a loss when asked for the angles of a right triangle. Forget it, and you'll be staring off into space, chewing your pencil, kicking your foot against the table leg, until, crack, you stub your toe. Better go soak it. Maybe now you'll remember. |
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Created on ... October 5, 2008