1. 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

2. 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

3. 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

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

5. You Try Find the missing side length. Leave answer in radical form. c2 c

6. You Try Find the missing side length. Leave answer in radical form. c14 c

7. You Try Find the missing side length. Leave answer in radical form. c21 c

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

9. 45o - 45o - 90o Triangle TheoremB C
45o s s

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

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

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

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

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

15. 30o - 60o - 90o Triangle TheoremD F E
60o 2n n
30o

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

17. Example
Find the value of x.
45o 12 x

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

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

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

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

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

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