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**UNIT QUESTION: What patterns can I find in right triangles?**

Math II UNIT QUESTION: What patterns can I find in right triangles? Standard: MM2G1, MM2G2 Today’s Question: How do I find the length of a side of a right triangle with only one side and an angle given? Standard: MM2G1.a

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**5.1 Special Right Triangles**

Learning Task – Part 1

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**5.1 Special Right Triangles**

You will be able to find the lengths of sides of special right triangles And

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**Special Right Triangles**

Short Leg:Long Leg:Hypotenuse

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**We will use a reference triangle to set up a proportion then solve.**

Right Triangle 60 2 1 30 This is our reference triangle for the triangle. We will use a reference triangle to set up a proportion then solve.

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Right Triangle 60 2x x 30

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Ex: 1 Solve for x and y. 60 8 2a a x 30 y a√3

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Solve for x and y Ex: 2 y a√3 30 x a 2a 24 60

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Ex: 3 Solve for x and y. 30 2a 14 y a√3 60 a x y = 7√3 x = 7

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Ex: Solve for x and y a x a√3 60 30 y 2a y = 10 x = 5

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**Perimeter = 27.71 inches a = 4.168 in., so 2a = 9.238 in. 2a a√3 a**

Extension Problem The altitude of an equilateral triangle is 8 inches. Find the perimeter of the triangle. 30° 2a a√3 8 60° a a = in., so 2a = in. Perimeter = inches

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Homework Page 155 #1-7 (odd), 14, 17-21

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CH 8 Right Triangles. Geometric Mean of 2 #’s If you are given two numbers a and b you can find the geometric mean. a # = # b 3 x = x 27 Ex ) 3 and 27.

CH 8 Right Triangles. Geometric Mean of 2 #’s If you are given two numbers a and b you can find the geometric mean. a # = # b 3 x = x 27 Ex ) 3 and 27.

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