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Standard: MCC9-12.G.SRT.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.Skills:SWBAT build upon their previous knowledge of similar triangles and of the Pythagorean Theorem to determine the side length ratios in special right triangles.There are 2 types of ____________________. One type of special _____________ triangle is a 45-45-90 ______________.What does 45-45-90 actually mean?A 45-45-90 triangle just means that that particular _________________ has a _____ degree angle, and 2 _______ degree angles45-45-90 triangles also have a special pattern!The ________ of the triangle are equal in length, meaning that one ______ is just as ________ as the other legThe ___________ is √2 times the length of the legI Do: Ms. Massih will complete the following 2 problems. Make sure you have your pencils down, mouths closed, and eyes up at the board while she is doing the problem. You will have time to copy down the problem after I have finished the problem.What is the value of each variable?What is the value of each variable?Let’s Do One Together!What is the length of the hypotenuse of a 45-45-90 triangle with a leg length of 5√3?Step 1: Draw a right triangle.Step 2: Label your right triangle, meaning put in the angles you know, and label your legs and hypotenuse as x, x, and x√2.Step 3: Now substitute in the values you know.Step 4: Solve for your variable.Step 5: Now write in all the sides for your triangle.Got It? Work quietly with your group members on the following 4 problems. We will review the answers as a class after. Remember, ask your group members before you ask me!Find the value of each variable.Find the value of each variable Find the value of each variableFind the value of each variable.Another type of _______________________________ triangle is a 30-60-90 __________________.The side across from the ____ degree angle xThe sides across from the 60 degree angle ______The side across from the _____ degree angle 2xI Do: Ms. Massih will complete the following 2 problems. Make sure you have your pencils down, mouths closed, and eyes up at the board while she is doing the problem. You will have time to copy down the problem after I have finished the problem.What is the value of d in simplest radical form? What is the value of f in simplest radical form?Let’s Do One Together! Find the value of each variable. If your answer is not an integer, express it in simplest radical form.Step 1: Label the right triangle above with the lengths for a 30-60-90 triangle. (Ex: x, 2x, x√3)Step 2: Write an equation with the sides you are given.Step 3: Now solve for your variable.Step 4: Plug in the value of the variable and find the remaining 2 sides.Got It? Work quietly with your group members on the following 4 problems. We will review the answers as a class after. Remember, ask your group members before you ask me!Find the value of each variable.18288033655002. INDEPENDENT PRACTICE: Work on the following problems using the information you just learned about 45-45-90 triangles and 30-60-90 triangles.9144046355000Directions: For each problem, what is the value of x? If your answer is not an integer, express it in simplest radical form.1. Find the value of x.Find the value of each variableFind the value of each variable.Find the value of each variable.Find the length of each side of the triangle. ................
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