1. Chapter 8 Right Triangles (page 284)
How can you apply right triangle facts to solve real life problems?

2. 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?

3. Lesson 8-5 The Tangent Ratio (page 305)
Trigonometry, comes from 2 Greek words,
which mean “ triangle measurement .”
Our study of trigonometry will be limited to
Right Triangle Trigonometry.

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

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

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

7. Definition of Tangent RatioB c a A b C
tangent of ∠A = tan A

8. Definition of Tangent RatioB c a A b C
tangent of ∠B = tan B

9. B c a A b C
remember

10. Example 1: Express tan A and tan B as ratios.
NOT B
tan A = ______
tan B = ______ 17 X
____ C A 15
What can we do now?
OH YEAH!
I know what I can do!

11. Example 1: Express tan A and tan B as ratios.
reciprocals 17 8
____ C A 15
Now we
can find the ratios!
Remember TOA.

12. Now try this with a calculator!
Example 2 The table on page 311 gives approximate decimal values of the tangent ratio for some angles.
“≈” means “is approximately equal to”
0.3640
(a) tan 20º ≈ ____________
(b) tan 87º ≈ ____________
Now try this with a calculator!

13. 0.3640 19.0811 (a) tan 20º ≈ ____________ (b) tan 87º ≈ ____________
To enter this in your calculator you will need to use the TAN function key.
Enter TAN(20) then press ENTER (=)
and round to 4 decimal places.
0.3640
(a) tan 20º ≈ ____________
(b) tan 87º ≈ ____________
Enter TAN(87) then press ENTER (=)
and round to 4 decimal places.

14. Now try this with a calculator!
Example 3 The table on page 311 can also be used to find an approximate angle measure given a tangent value.
“≈” means “is approximately equal to”
30º
(a) tan _______ ≈
(b) tan _______ ≈
76º
Now try this with a calculator!

15. 30º 76º (a) tan _______ ≈ 0.5774 (b) tan _______ ≈ 4.0108
To enter this in your calculator you will need to use the inverse key or 2nd function key.
Enter TAN-1(.5774) then press ENTER (=)
and round to the nearest degree
30º
(a) tan _______ ≈
(b) tan _______ ≈
Enter TAN-1(4.0108) then press ENTER (=)
and round to the nearest degree
76º

16. Example 4 (a) Find the value of x to the nearest tenth. x ≈ ________
18.8 x
You can type this in your calculator!
37º 25

17. Example 4 (b) Find the value of x to the nearest tenth. x ≈ ________
9.2 x 3
72º

18. Example 4 (c) Find the value of y to the nearest degree. y ≈ ________
51º 5
Type this in your calculator! yº 4

19. Example 4 (d) Find the value of y to the nearest degree. y ≈ ________
32º 8 x yº 5

20. How can you apply right triangle facts to solve real life problems?
Assignment
Written Exercises on pages 308 & 309
RECOMMENDED: 1 to 11 odd numbers, 25
REQUIRED: 13 to 23 odd numbers, 27
PK Hint for your HW.
For #19 on page 309 you should first read
Example 3 on page 306.
How can you apply right triangle facts to solve real life problems?

25. Page 309 #19
The grade of a road is 7%.
What angle does the road make with the horizontal?
ROAD
vertical
ANGLE
horizontal