1. Lesson Objective: Use right triangles to evaluate trig functions.
Date:
4.3(a) Notes: Trig. Ratios
Lesson Objective: Use right triangles to evaluate trig functions.
CCSS: F-TF Extend the domain of tri­go­no­me­tric functions using the unit circle.
You will need: calculator

2. Lesson 1: Trig. Definitions
Trigonometric (trig) Ratio: A ratio of 2 sides of a right triangle.
Reference Angle: The acute angle we are referring to or are using.
Opposite Leg: The leg across from the / that is not the hypotenuse.
Adjacent Leg: The leg next to the / that is not the hypotenuse.
Hypotenuse: The side opposite the right / .

3. Lesson 1: Trig. Definitions BC is _________________ / A.
BC is _________________ / A.
AB is ________________ / A.
AC is the ___________________. A
B C

4. Lesson 2: SOH-CAH-TOA Game
Draw the figure. Choose the correct answer. Write each question and answer in your notes. Z
Y X

5. Lesson 2: SOH-CAH-TOA Game A. Opposite / X
A. Opposite / X Z
Y X

6. Lesson 2: SOH-CAH-TOA Game B. Adjacent to / X
B. Adjacent to / X Z
Y X

7. Lesson 2: SOH-CAH-TOA Game C. Hypotenuse
C. Hypotenuse Z
Y X

8. Lesson 2: SOH-CAH-TOA Game D. Adjacent to Leg 1
D. Adjacent to Leg 1 Z
Y X

9. Lesson 2: SOH-CAH-TOA Game E. Opposite / Y
E. Opposite / Y Z
Y X

10. Lesson 2: SOH-CAH-TOA Game F. Opposite Leg 1
F. Opposite Leg 1 Z
Y X

11. Lesson 2: SOH-CAH-TOA Game G. Opposite / Z
G. Opposite / Z Z
Y X

12. Lesson 2: SOH-CAH-TOA Game H. Adjacent to Leg 3
H. Adjacent to Leg 3 Z
Y X

13. Lesson 2: SOH-CAH-TOA Game I. Adjacent to / Z
I. Adjacent to / Z Z
Y X

14. Lesson 2: SOH-CAH-TOA Game J. Opposite / Y
J. Opposite / Y Z
Y X

15. Lesson 2: SOH-CAH-TOA Game K. Opposite Leg 3
K. Opposite Leg 3 Z
Y X

16. Lesson 3: Trig. Ratios
“SOH”

17. Lesson 3: Trig. Ratios
“CAH”

18. Lesson 3: Trig. Ratios
“TOA”

19. COSECANT = 1 = Hypotenuse csc SIN Opposite SECANT = 1 = Hypotenuse
Lesson 3: Trig. Ratios
“SOH-CAH-TOA”
COSECANT = = Hypotenuse
csc SIN Opposite
SECANT = = Hypotenuse
sec COS Adjacent
COTANGENT = = Adjacent
cot TAN Opposite

20. Find the values of the 6 trig. functions of θ.
Lesson 3: Trig. Ratios
Find the values of the 6 trig. functions of θ.

21. Lesson 4: Angle of Elevation and Depression

22. Lesson 4: Angle of Elevation and Depression
A. Suppose the car is 150 feet from the building and the observer’s angle of depres­sion is 40°. What is the distance of the line of sight below the observer?  

23. Lesson 4: Angle of Elevation and Depression
B Sighting the top of a building, a surveyor mea­sured the angle of elevation to be 22°. The transit through which the surveyor sights the building’s angle of elevation is 5 feet above the ground and 300 feet from the building. Draw a diagram, then find the building’s height. 

24. Find the values of the 6 trig. functions of the other acute angle, β,.
4.3(a): Do I Get It? Yes or No
Find the values of the 6 trig. functions
of the other acute angle, β,.

25. 4.3(a): Do I Get It? Continued A surveyor is standing 115 feet
A surveyor is
standing 115 feet
from the base of the
Washington Monu-
ment. The surveyor
measures the angle
of elevation to the
top of the monu-
ment as 78.3°. How
Tall is the Washington
Monument?

26. 4.3(a): Do I Get It? Continued
3. Find the length c of the skateboard ramp.