Unit 8 Lesson 9.4A Special Right Triangles

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Special Right Triangles

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Presentation transcript:

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

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

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

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

You Try Find the missing side length. Leave answer in radical form. 2 c 45o 45o

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

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

45o - 45o - 90o Triangle Theorem B C 45o s s

You Try Find the missing side length. Leave answer in radical form. 2 60o 30o 4

You Try Find the missing side length. Leave answer in radical form. 7 60o 30o c

You Try Find the missing side length. Leave answer in radical form. 42

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

30o - 60o - 90o Triangle Theorem D F E 60o 2n n 30o

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”

Example Find the value of x.

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

Example Find the value of x. 45o 12 x

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

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

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

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