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**Unit 8 Lesson 9.4A Special Right Triangles**

CCSS Lesson Goals G-SRT 8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. G-SRT 8.1: Derive and use the trigonometric ratios for special right triangles (30°,60°,90°and 45°,45°,90°). Define a special right triangle Identify the patterns in special right triangles. Use the special right triangle theorems to find missing side lengths in right triangles. ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

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**Why are special right triangle theorems useful if we have the Pythagorean Theorem?**

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**Definition Special Right Triangles**

not in notes Definition Special Right Triangles A right triangle with acute angles of 45o and 45o. A right triangle with acute angles of 30o and 60o. D F E A B C 60o 45o 30o 45o

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You Try (not in notes) Find the missing angle measures. 7 xo xo

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**You Try Find the missing side length. Leave answer in radical form.**

2 c 45o 45o

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You Try Find c. Leave answer in radical form. 7 c 45o 45o

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7 2 45o 45o 45o 45o 10 45o 45o 45o 45o

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**45o - 45o - 90o Triangle Theorem**

B C 45o s s

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**You Try Find the missing side length. Leave answer in radical form.**

2 60o 30o 4

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**You Try Find the missing side length. Leave answer in radical form.**

7 60o 30o c

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**You Try Find the missing side length. Leave answer in radical form.**

42

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21 60o 30o 2 60o 30o 7 60o 30o 14 42 4 60o 30o 3 60o 30o 8 6 4

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**30o - 60o - 90o Triangle Theorem**

D F E 60o 2n n 30o

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**Steps to help in solving**

Step 1: Place the pattern on the triangle (make sure you use a different variable than the ones on the triangle) Step 2: Setup 3 different equations based on what you have on each side of the triangle Step 3: Solve the equation that only has one variable Step 4: Use the answer from step 3 to solve other two sides. Please note not all answers will be “pretty”

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Example Find the value of x.

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Example Find the value of x. 5 5 45o x

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Example Find the value of x. 45o 12 x

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Example Find the value of f and g. 60o f 4 30o g

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Example 5 Find the value of m and n. m 30o n 60o

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Summary Why are special right triangle theorems useful if we have the Pythagorean Theorem?

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Today’s Assignment p. 554: 1 – 14, 43, 45, 47 – 49

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