1. Chapter 9 Right Triangle Trigonometry
DEFINE Sine, Cosine, & Tangent Ratios
Use Ratios to SOLVE height and distance problems
APPLY Vectors to Trigonometry Problems

2. Section 9 – 1 & 9 – 2 Tangent, Sine & Cosine Ratios
Objectives:
To write sine, cosine, and tangent ratios
To find missing side lengths of right triangles using Trig Ratios
To find missing angle measure of right triangles using Trig Ratios

3. Tangent Ratio
Tangent of ∠𝑨= 𝒍𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒍𝒆𝒈 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 ∠𝑨 𝒍𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒍𝒆𝒈 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝒕𝒐 ∠𝑨 Abbreviated Form: tan A = 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕

4. Sine Ratio
Sine of ∠𝑨= 𝒍𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒍𝒆𝒈 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 ∠𝑨 𝒍𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝑯𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆 Abbreviated Form: sin A = 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆

5. Cosine Ratio
Cosine of ∠𝑨= 𝒍𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒍𝒆𝒈 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 ∠𝑨 𝒍𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝑯𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆 Abbreviated Form: cos A = 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆

6. S O H C A H T O A INE OSINE ANGENT PPOSITE YPOTENUSE DJACENT YPOTENUSE

7. Example 1 Writing Tangent Ratios
Write the Trig Ratios for each acute angle. A) B)
How is tan K related to tan J?

8. How are Sin X and Cos Y related?
Write the Trig Ratios for each acute angle. C) D)
How are Sin X and Cos Y related?

9. HOMEWORK
Kuta Ditto – Trig Ratios

10. Section 9 – 1 & 9 – 2 Continued…
Objectives:
To find missing side lengths of right triangles using Trig Ratios

11. Example 2 Finding Side Lengths
Find the value of x. Round to the nearest tenth. A)

12. B) C)

13. D) E)

14. F) G)

15. H) I)

16. HOMEWORK
KUTA Ditto; Solving Right Triangles

17. Section 9 – 1 & 9 – 2 Continued…
Objectives:
To find missing angles measures of right triangles using Trig Ratios

18. Example 3 Finding Angle Measures
Find the m ∠ X or m ∠ Y to the nearest degree. A) B)

19. C) D)

20. E) F)