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

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Presentation transcript:

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

5.1 Special Right Triangles Learning Task – Part 1

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

30-60-90

Special Right Triangles Short Leg:Long Leg:Hypotenuse

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

30-60-90 Right Triangle 60 2x x 30

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

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

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

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

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

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