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Unformatted text preview: 306090 Triangles
A 306090 triangle is a triangle with angles of 30, 60, and 90. What makes it special is the specific pattern that the lengths of the sides of a 306090 triangle follow. Suppose the short leg, opposite the 30 angle, has length x. Then the hypotenuse has length 2x, and the long leg, opposite the 60 degree angle, has length x . The sides of every 306090 triangle will follow this 1 : 2 : ratio. The constant ratio in the lengths of the sides of a 306090 triangle means that if you know the length of one side in the triangle, you immediately know the lengths of all the sides. If, for example, you know that the side opposite the 30 angle is 2 meters long, then by using the 1 : 2 : ratio, you know that the hypotenuse is 4 meters long and the leg opposite the 60 angle is 2 meters. On the Math IIC you will quite often encounter a question that will present you with an unnamed 306090 triangle, allowing you to use your knowledge of this special triangle. You could solve these questions by using the Pythagorean theorem, but that method takes a lot longer than simply knowing the proper 306090 ratio. The key is to be aware that there are 306090 triangles lurking out there and to strike when you see one. ...
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