ࡱ> fhe{n'` Rbjbj 42R ,((((Lt$@ $ q!q!q!!$#$#$#$#$#$#$$%h'G$q!m!q!q!q!G$ \$###q!   !$#q!!$###  d(w({!B#!$r$0$#("(#(#<q!q!#q!q!q!q!q!G$G$# q!q!q!$q!q!q!q!@ @ @ $ d@ @ @ dD,( Investigation: Some Triangles are Special  Part 1 45-45-90 Triangles Step 1: Find the value of each variable. Round your answers to the nearest thousandth. Why are the figures 45-45-90 triangles? a. b.   Step 2: Find the ratio of hypotenuse to leg of each triangle. So what is the relationship between the length of a leg and its hypotenuse in a 45-45-90 triangle? Step 3: What is the approximate value of  EMBED Equation.3 ? How is this related to 45-45-90 triangles? Step 4: In a 45-45-90 triangle, When finding the length of a hypotenuse, you should ___________(multiply/divide) the length of the given legs by  EMBED Equation.3 . When finding the length of the legs, you should _____________(multiply/divide) the length of the given hypotenuse by  EMBED Equation.3 . Step 5: Practice. Find the length of all the missing sides, in simplest form. a. b. c. d.     Part 2 Rationalizing the denominator In mathematics, there are certain rules that you need to follow, like fractions and radicals must be in simplest form, for example. There is also another rule that radicals (which are irrational numbers) may not remain in the denominator. They may only be in the numerator. So we have a process called rationalizing the denominator. Step 1: What is  EMBED Equation.3 ? What is  EMBED Equation.3 ?  EMBED Equation.3 ? So what happens when you multiply a square root by itself? Step 2: We will use this idea to rationalize  EMBED Equation.3 .  EMBED Equation.3  Step 3: Rationalize the following. a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  Step 4: Why do we need to know this? Well, try to solve these problems. Put your answer in simplest form. a. b. c.    Part 3 30-60-90 Triangles Step 1: Find the value of the variables. Round your answers to the nearest thousandth. What kind of triangle do two 30-60-90 triangles make? a. b.   Step 2: In problem a, what is the ratio between hypotenuse and x? What is the ratio between y and x? In problem b, what is the ratio between the hypotenuse and 9? What is the ratio between the y and 9? Step 3: What is the approximate value of EMBED Equation.3 ? How is this related to 30-60-90 triangles? What number is bigger,  EMBED Equation.3  or 2? Step 4: Label the triangles below using the words hypotenuse, short leg, long leg.  Step 5: In 30-60-90 triangles, When finding the length of the hypotenuse, you should ___________(multiply/divide) the ____________(short leg/long leg) by the scale factor of ________. When finding the length of the long leg, you should ___________(multiply/divide) the ____________(hypotenuse/short leg) by the scale factor of _________. When finding the length of the short leg, you should ___________(multiply/divide) the hypotenuse by ______. When finding the length of the short leg, you should ___________(multiply/divide) the long leg by ______. Step 6: Practice. Find the length of the missing sides of the triangles. Leave your answer in simplest form. a. b. c.  d. e. f.    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