1. Right Triangle 3 Tangent, Sine and Cosine
Finding the length of a side of a Right Triangle

2. Trigonometric Ratios
In this activity we will learn about the ratios of the lengths of the sides of a right triangle.
The first ratio is called the Tangent ratio. It is defined as: A B C
Tangent of B = leg opposite B
leg adjacent B
This is abbreviated as:
Tan B = opp
adj

3. Find the tangent ratio for B
Tangent Examples
Find the tangent ratio for B A B C 3 4 5
Tan B = opp
adj
Tan B =3 4
Tan B = .75

4. Sine of B = leg opposite B hypotenuse
The Second Ratio that you will discover is called the Sine Ratio. It is defined as:
Sine of B = leg opposite B
hypotenuse A B C
This is abbreviated as:
SinB = opp
hyp

5. Find the sine ratio for B
Sine Examples A B C 5 3 4
Find the sine ratio for B
Sin B = opp
hyp
Sin B = 3 5
Sin B = .6

6. Cosine of B = leg adjacent B hypotenuse
The third ratio to discover is called the Cosine ratio. It is defined as:
Cosine of B = leg adjacent B A B C
hypotenuse
This is abbreviated as:
Cos B = adj
hyp

7. Find the Cosine ratio for B
Cosine Examples
Find the Cosine ratio for B A B C 4 5 3
Cos = adj
hyp
Cos B = 4 5
Cos B = .8

8. Trigonometric Ratios
Ask your teacher to tell you the story of Chief SohCahToa!
On your worksheet
do # 

9. Trigonometric Ratios
You can use your scientific calculator to find the trigonometric ratio associated with an angle. Your calculator must be in degrees.
.4848
Sin 29 = _____
On your worksheet do # 11 – 16.
You can use the inverse key on your scientific calculator to find the angle associated with a trigonometric ratio. 15
Tan _____° = .2679
On your worksheet do # 17-22

10. Trigonometric Ratios
We Can use Trig ratios to find missing sides of right triangles.
Tangent
Which trig ratio should be used?
What is the Setup? X
37°
250
Tan 37° = X
250
X = 188.4

11. What trig ratio should be used to find the measure of X?
Trigonometric Ratios
What if you need to find an angle of a right triangle? We can use trig ratios and the inverse key.
What trig ratio should be used to find the measure of X? 17 15 X
Cosine
What is the setup?
Cos X = 15 17
X = Cos-1 (1517)
X = 28°

12. Practice Problems Find the missing side5
40 a 1.
Tan 40° = a / 5
Tan 40° (5) = a
.8391(5) = a
a = 4.195 2.
120 x
63
Sin 63° = 120 x
x (Sin 63°) = 120
x =
sin 63°
x =

13. 3. Cos 18° = x 2500 Cos 18° (2500) = x x = 2377.6 4. a Tan 15° = 6 a
18
2500 x
Cos 18° = x
2500
Cos 18° (2500) = x
x = 4. 6
15 a
Tan 15° = 6 a
a (Tan 15° ) = 6
a =
(Tan 15°)
a = 22.39

14. Find the missing angles5. 3 4 x
Tan x = 4/ 3
x = Tan -1 (4/3)
x = 53.13°
x = 53° 15 x 10 6.
Cos x = 10 / 15
x = cos -1 (10 / 15)
x = °
x = 48°

15. 7. Sin x = 2 / 12 x = sin -1 (2 / 12) x = 9.6 ° x = 10 ° 8.5 x
Tan x = 5 / 12
x = Tan-1 (5/12)
x = 22.61°
x = 23°

16. Homework:
p.529(22-26 even,32-36 even,37-43)
p.538(20,30-35)