Unit 6 Lesson 2 Special Right Triangles

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Presentation transcript:

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

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

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. c 2 c

You Try Find the missing side length. Leave answer in radical form. c 14 c

You Try Find the missing side length. Leave answer in radical form. c 21 c

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

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

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

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

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

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

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

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

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

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

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

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