1. 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

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

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.2 c
45o
45o

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

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

8. 45o - 45o - 90o Triangle TheoremB C
45o s s

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

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

13. 30o - 60o - 90o Triangle TheoremD F E
60o 2n n
30o

14. 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”

15. Example
Find the value of x.

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

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

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