There are multiple methods that can be used to find the sides and angles of a triangle. Examples include Special Rights (30, 60, 90 and 45, 45, 90), SOHCAHTOA, and the law of sines and cosines. These are very helpful methods. I will explain to my best ability how to do all three of these with examples at the end.
The first example special rights are used only with right triangles. To do this method you have to have angle measures of 30, 60, and 90, or 45, 45, and 90. There is a “stencil” that goes with these degrees. In the 30, 60, 90 triangle the side opposite the 30 degrees is “S”. The side opposite of the 90 degrees is “2S”. Lastly the side opposing the 60 degree angle is “S radical 3”. Let’s say you were given “S” you would multiply that by two to find the value of the side opposite of the 90 degrees. To find the side corresponding with 60 degrees you then take the value of “S” and set it equal to ”S √3”. Then you would have to move the radical three over to the other side. Finally you divide by three to get the answer. With a 45, 45, 90 triangle, the side the side corresponding with the 90 iss√(2&2). The sides corresponding with the 45 degrees angles are both “S”
Next we have the acronym SOHCAHTOA. A way to remember it is: some old horse caught another horse tripping over apples. This method is used to find angles when given the sides of a triangle, unlike special rights. The acronym stands for sine- opposite divided by the hypotenuse, cosine- adjacent divided by the hypotenuse, and tangent- opposite divided by adjacent. This method also can only be used with right triangles. When doing a problem like this it will state which method you should use (sine, cosine, and tangent). Let’s start with sine first.
Sine is listed above as OPPOSITE ÷ HYPOTENUSE. The side corresponding with the 90 degree angle (the only angle given) 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 left is the adjacent side. Then you do opposite over hypotenuse to get the degree of “X”. Since all triangles equal 180 degrees you then can find the third degree, by adding the two given degrees and subtracting that by 180.
Cosine is listed above as ADJECENT÷HYPOTENUSE....