1. Tangent Ratio

2. Labelling Right Triangles
Theta: the symbol we will use to represent an unknown angle. Ө
Hypotenuse
Adjacent
Opposite Ө

3. Definitions
Hypotenuse: The longest side of a right triangle. It is always across from the 90 degree angle. Adjacent side: Always the side that is attached to or touching the theta symbol Opposite Side: Always the side that is across from the theta symbol. It is not touching Ө Ө

4. Ex 1) Label the triangle with HYP, ADJ, and OPP
Hypotenuse
Opposite
Adjacent Ө

5. Ex 2) Place Ө in the correct angle.
Adjacent
Opposite
Hypotenuse Ө
HYP OPP
ADJ Ө

6. Ratios
When we have a right triangle, and we have 1 given side and 1 given angle, and we need to find the missing sides, we use SIN, COS or TAN.
Step 1: label the sides HYP OPP ADJ
Step 2: Choose either Sin, Cos or Tan (depending on which side is given and which side you need to find)
Step 3: Write out the formula with Sin, Cos or Tan
Step 4: Insert the information that has been given in the question (the side length and the angle).

7. Tangent Ratio (TAN) Tan θ = Opposite side Adjacent side
If you have a triangle, and you are given a measurement and a variable for the OPPOSITE SIDE and the ADJACENT SIDE, then you need to use the TAN function on your calculator to find the missing side.

8. Trigonometric Ratios

9. Tangent Ratio Tan A = Opposite Adjacent Tan 45o = x cm 13cm HYP ADJ
Step 1: Label sides
Step 2: Choose Sin, Cos, Tan
Step 3: Write out formula
Step 4: Insert the given information
(A or Ө is always an angle)
Step 5: Find the missing side (x). Use cross-multiplication
Tan A = Opposite
Adjacent A 45
13cm
B C
x cm
HYP
ADJ
Tan 45o = x cm
13cm
OPP

10. Ex 1) Write an equation that you can use to find the value of x.
Tan C= Opp
Adj
Tan 30= x cm
11cm D
x cm F E A
X cm
B C
11 cm
ADJ
OPP
OPP
ADJ
Tan F= Opp
Adj
Tan 30= 5 cm
x cm

11. Ex 2) Find Tan A. Keep your answer as a fraction.
Tan A = Opposite
Adjacent A
5cm √74 cm
B C
7cm
Tan A= 7cm
5cm
ADJ
OPP B
6cm 6√3 cm
A cm C

12. Ex 3) Find the value of x. 45
15cm x
32 cm 60 x

13. Class Work
Page 560 #1, 2, 4 Page 561 #13-15

14. Sine and Cosine Ratios

15. Sine Ratio Sin Ө = Opposite Side Hypotenuse
If you have a triangle, and you are given a measurement and a variable for the OPPOSITE SIDE and the HYPOTENUSE, then you need to use the SIN function.
Sin Ө = Opposite Side
Hypotenuse

16. Trigonometric Ratios

17. Ex 1) Write an equation for Sin A. Find the value of x.
Sin A = Opp
Hyp
Sin 30 = x cm
10 cm
10 cm (Sin 30) = x cm
1/2 x 10 = x
x = 5 cm A 30
10cm
B C
x cm

18. Ex 1) Write an equation for Sin A. Find the value of x.B
X cm 12cm 60
C A

19. Cosine Ratio Cos Ө = Adjacent Side Hypotenuse
If you have a triangle, and you are given a measurement and a variable for the HYPOTENUSE and the ADJACENT SIDE, then you need to use the COS function.
Cos Ө = Adjacent Side
Hypotenuse

20. Trigonometric Ratios

21. Write an equation for Cos A
7cm cm
B C B
11cm
C A
5cm

22. Ex 1) Write an equation for Cos A. Find the value of x. 45
7cm x cm
B C
Cos A = ADJ
HYP
Cos 45 = 7cm
x cm
√2 = 7 x
√2 x = 14
x=7√2

23. Ex 1) Find the value of x. Choose Sin, Cos or Tan.B
11cm
6 cm 30
C A
x cm

24. Ex 2) Write equations for Sin A and Cos A.
A 15cm B
17cm 8cm C A
10 cm cm
B cm C

25. TOA Tan A= Opp Adj SOH Sin A = Opp Hyp CAH Cos A = Adj
Trigonometric Ratios
SOH Sin A = Opp
Hyp
CAH Cos A = Adj
TOA Tan A= Opp
Adj

26. Class Work
Page 563 #1-3
Page 564 # 4-6
Page 566 #11-16