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Explore the properties of 45-45-90 and 30-60-90 special right triangles through interactive entries and practice exercises. Discover how to find side lengths using reference triangles and equations.
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Interactive Notebook EntriesTable of Contentspg. 21 Special Right Triangles NotesPg. 22 Special Right TrianglesPractice
7.3 Special Right Triangles *You will be able to find the lengths of sides of special right triangles 45-45-90 And 30-60-90
Special Right Triangles Leg:Leg:Hypotenuse Short Leg:Long Leg:Hypotenuse
We will use a reference triangle to set up an equation then solve. In a 45-45-90 triangle… LEGS ARE THE SAME LENGTH
45-45-90 Right Triangle 1 1 This is our reference triangle for the 45-45-90.
Example 1: Solve for x x 3 Hyp = • Leg 3
Example 2: Solve for x x 5 5 Hyp = • Leg
Example: 3 Solve for x Hyp = • Leg 45 3 x
We will use a reference triangle to set up an equation then solve. 30-60-90 Right Triangle 60 2 1 30 This is our reference triangle for the 30-60-90 triangle.
30-60-90 Right Triangle 60 2x x 30
Example: 1 Solve for x and y 60 8 x 30 y
Solve for x Example 2: 30 x 24 60
Example: 3 Solve for x and y 30 14 y 60 x 14 = 2x 7 = x
Example 4: Solve for x and y x 60 30 y y = 10 5 = x