Angle, Side Length of a TriangleDate: 9/4/96 at 17:19:5 From: Robert Inman Subject: Angle, Side Length of a Triangle Hi Dr. Math, What is the relation between the angles of a triangle and the length of its sides? For example, if I know that a triangle has a 90 degree angle, I know the length of one leg, and the angle between that leg and the hypotenuse, how do I determine the length of the other leg? Date: 9/4/96 at 18:53:10 From: Doctor Tom Subject: Re: Angle, Side Length of a Triangle Hi Robert, One simple relation is that the bigger the angle, the bigger the side opposite it. There's an exact relation called the "law of sines". Assume that your triangle has sides of length A, B, and C. Assume also that the angle opposite side A is a, opposite B is b, and opposite C is c. The law of sines states: sin a sin b sin c ----- = ----- = ----- A B C Unfortunately, it uses trigonometry. You can look up the values of the sines of angles in tables, or using some calculators. The "law of cosines" is also sometimes valuable. It states that: C^2 = A^2 + B^2 - 2ABcos c with the same labels as above. "cos" is the cosine function, and I use "^" to indicate an exponent: "C^2" is "C squared". "Trigonometry" comes from the Greek: "trig" - triangle, and "metry" - measurement. That's exactly what you're trying to do, right? -Doctor Tom, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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