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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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Learning Task – Part 1

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You will be able to find the lengths of sides of special right triangles 30-60-90 And 45-45-90

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Short Leg:Long Leg:Hypotenuse

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30-60-90 Right Triangle 1 2 30 60 This is our reference triangle for the 30-60-90 triangle. We will use a reference triangle to set up a proportion then solve.

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30-60-90 Right Triangle x 2x2x 30 60

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

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

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

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60 30 x x = 5 Ex: 4 Solve for x and y y y = 10 2a a a√3

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a = 4.168 in., so 2a = 9.238 in. Extension Problem The altitude of an equilateral triangle is 8 inches. Find the perimeter of the triangle. 2a a 8 60° 30° a√3 Perimeter = 27.71 inches

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

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