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**Unit 6 Lesson 2 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°). 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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**Previously on Geometry Previously on Geometry**

The Pythagorean Theorem is used to find missing side lengths in right triangles. Isosceles triangles have two congruent sides and two congruent angles. The acute angles of a right triangle are complementary. Previously on Geometry Previously on Geometry 8 17 b x y

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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. c**

2 c

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

14 c

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

21 c

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You Try Find c. Leave answer in radical form. s c

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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.**

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

2 60o 30o 4

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You Try Find c in terms of a. a 60o 30o c

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You Try (not in notes) Find a in terms of c. a 60o 30o c

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

D F E 60o 2n n 30o

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

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Example An equilateral triangle has side length 8 feet. Estimate the area. 8 ft

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Example Find the exact values of p, q, r, s, t, u, v, and w.

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Summary How are the special right triangle theorems related to the Pythagorean Theorem?

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Today’s Assignment p. 554: 12 – 20, 24, 25, 30 – 34

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