1. How can you apply right triangle facts to solve real life problems?
Trigonometry
Essential Question
How can you apply right triangle facts to solve real life problems?

2. Lesson 8-6 The Sine and Cosine Ratios (page 312)
The sine ratio and cosine ratio relate the legs to
the hypotenuse .

3. Review! hypotenuse leg leg The tangent ratio is the ratio
of the lengths of the legs . B
hypotenuse
Review! c
leg a A b C
leg

4. opposite leg vs adjacent legB
In relationship to angle A … c
opposite leg a A b C
adjacent leg

5. opposite leg vs adjacent legB
In relationship to angle B … c
adjacent leg a A b C
opposite leg

6. Definition of Tangent RatioB
Review! c a A b C
tangent of ∠A = tan A

7. Definition of Sine RatioB c a A b C
sine of ∠A = sin A

8. Definition of Cosine RatioB c a A b C
cosine of ∠A = cos A

9. B c a A b C

10. REMEMBER! B
DO NOT
FORGET! c a A b C
SOH CAH TOA

11. Example 1 Express the sine and cosine of ∠A & ∠B as ratios.13 5
____ C A 12 A
sin A = ______ (b) cos A = ______
(c) sin B = ______ (d) cos B = ______

12. Example 1 Express the sine and cosine of ∠A & ∠B as ratios.13 A 5
____ C A 12 O
sin A = ______ (b) cos A = ______
(c) sin B = ______ (d) cos B = ______

13. Now try this with a calculator!
Example 2 Use the trigonometry table, then use a calculator to find the approximate decimal values.
“≈” means “is approximately equal to”
0.3746
Please note
that these are only
APPROXIMATIONS!
(a) sin 22º ≈ __________
(b) cos 79º ≈ __________
0.1908
Now try this with a calculator!

14. 0.3746 0.1908 (a) sin 22º ≈ ____________ (b) cos 79º ≈ ____________
To enter this in your calculator you will need to use the SIN or COS function key.
Enter SIN(22) then press ENTER (=)
and round to 4 decimal places.
0.3746
(a) sin 22º ≈ ____________
(b) cos 79º ≈ ____________
Enter COS(79) then press ENTER (=)
and round to 4 decimal places.
0.1908

15. Now try this with a calculator!
… Example 2 Use the trigonometry table to find the approximate angle measures.
“≈” means “is approximately equal to”
61º
Please note
that these are only
APPROXIMATIONS!
(c) sin ______ ≈
(d) cos _______ ≈
39º
Now try this with a calculator!

16. 61º 39º (c) sin ______ ≈ 0.8746 (d) cos _______ ≈ 0.7771
To enter this in your calculator you will need to use the inverse key or 2nd function key.
Enter SIN-1(.8746) then press ENTER (=)
and round to the nearest degree
61º
(c) sin ______ ≈
(d) cos _______ ≈
Enter COS-1(.7771) then press ENTER (=)
and round to the nearest degree
39º

17. What can you say about the values for the sine or cosine of an angle?
The values for sine and cosine …
Think about it …
if the hypotenuse is the longest side
and it is the denominator of the ratios,
then it …
… will always be less than 1.
Enter SIN-1(1.5) then press ENTER (=) …

18. Example 3 (a) Find the value of x and y to the nearest integer
Example 3 (a) Find the value of x and y to the nearest integer. x ≈ ______ y ≈ ______ 52 84 x
38º y

19. Example 3 (a) Find the value of x and y to the nearest integer
Example 3 (a) Find the value of x and y to the nearest integer. x ≈ ______ y ≈ ______ 52 66 84 x
38º y

20. Example 3 (b) Find the value of x and y to the nearest integer
Example 3 (b) Find the value of x and y to the nearest integer. x ≈ ______ y ≈ ______ 12 1 x x y 1
55º 7 7 14

21. Example 3 (b) Find the value of x and y to the nearest integer
Example 3 (b) Find the value of x and y to the nearest integer. x ≈ ______ y ≈ ______ 12 10 x x y
55º 7 7 14

22. Example 4 (a): Find “n” to the nearest degree. n ≈ ______44 nº O 14 20 H

23. Example 4 (b) Find the measures of the 3 angles of a 3-4-5 ∆.

24. Example 4 (b) Find the measures of the 3 angles of a 3-4-5 ∆.
∴ a right triangle.
continue

25. Example 4 (b) Find the measures of the 3 angles of a 3-4-5 ∆.
90º - 53º = 37º
∴ the angle measures are 37º, 53º, & 90º.

26. How can you apply right triangle facts to solve real life problems?
Assignment
Written Exercises on pages 314 to 316
RECOMMENDED: 1 to 9 odd numbers
REQUIRED: 11 to 23 odd numbers
Worksheet on Lessons 8-5 & 8-6
The Sine, Cosine, and Tangent Ratios
How can you apply right triangle facts to solve real life problems?