There are several methods that can be used to find the sides and angles of a triangle, such as special right triangles (30, 60, 90 and 45, 45, 90), SOHCAHTOA, and the Law of Sines and Cosines. These methods are very useful. I'll explain how to use all three with examples at the end. The first example, Special Right Triangles, is used only with right triangles. To use this method, you must have angle measurements of 30, 60, and 90 or 45, 45, and 90. There is a "stencil" that accompanies these degrees. In the 30-60-90 triangle the side opposite the 30 degrees is "S". The side opposite the 90 degrees is "2S". Finally, the side opposite the 60 degree angle is "S radical 3". Let's say you were given "S". You would multiply this by two to find the value of the side opposite 90 degrees. To find the side corresponding to 60 degrees, then take the value of "S" and set it equal to "S √3". Then you should move the three radicals to the other side. Finally, divide by three to get your answer. With a 45-45-90 triangle the side corresponding to 90 is s√2. The sides corresponding to the 45 degree angles are both "S". Next, we have the acronym SOHCAHTOA. One way to remember it is, "An old hippie caught another hippie on acid." This method is used to find angles when the sides of a triangle are given, unlike special right triangles. The acronym stands for sine (opposites divided by the hypotenuse), cosine (adjacent divided by the hypotenuse), and tangent (opposites divided by the adjacent). This method can also be used with right triangles only. When solving a problem like this, you will be told which method you should use (sine, cosine, or tangent). Let's start with the breasts first. The sine is listed above as OPPOSITE ÷ HYPOTENUSE. The side corresponding to the 90 degree angle (the only given angle) is always the hypotenuse of the triangle. The angle you are solving for is "X" and its corresponding side is always the opposite side of the triangle. Whichever side is the left is the adjacent side. Then do the reverse on the hypotenuse to get the degree of "X". Since all triangles are equal to 180 degrees, you can find the third degree by adding the two degrees shown and subtracting them by 180.