Right Triangle 3
Tangent, Sine and
Cosine
Finding the length of a side
of a Right Triangle
•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:
C
Tangent of B = leg opposite B
leg adjacent B
This is abbreviated as:
Tan B = opp
adj
B
A
•Find the tangent ratio for B
C
Tan B = opp
adj
Tan B =3
4
Tan B = .75
5
B
3
4
A
•The Second Ratio that you will discover is called the Sine
Ratio. It is defined as:
Sine of B = leg opposite B
hypotenuse
This is abbreviated as:
SinB = opp
hyp
C
B
A
C
•Find the sine ratio for B
5
Sin B = opp
hyp
Sin B = 3
5
Sin B = .6
B
3
4
A
•The third ratio to discover is called the Cosine
ratio. It is defined as:
Cosine of B = leg adjacent B
hypotenuse
This is abbreviated as:
Cos B = adj
hyp
B
C
A
•Find the Cosine ratio for B
C
Cos = adj
hyp
Cos B = 4
5
Cos B = .8
5
B
3
4
A
Ask your teacher to tell you the story of
Chief
SohCahToa!
On your worksheet
do # 1 - 10
•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
•We Can use Trig ratios to find missing sides of right
triangles.
•Which trig ratio should be used?
Tangent
•What is the Setup?
Tan 37° = X
250
X = 188.4
X
250
37°
•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?
Cosine
X
•What is the setup?
17
15
Cos X = 15
17
X = Cos-1 (1517)
X = 28°
Practice Problems
Find the missing side
1.
Tan 40° = a / 5
40
Tan 40° (5) = a
5
.8391(5) = a
a
a = 4.195
Sin 63° = 120
2.
x
x
x (Sin 63°) = 120
120
x = 120
63
sin 63°
x = 134.679
3.
Cos 18° =
2500
x
2500
Cos 18° (2500) = x
18
x = 2377.6
x
4.
a
Tan 15° = 6
15
a
6
a (Tan 15° ) = 6
a
=
6
(Tan 15°)
a = 22.39
Find the missing angles
5.
3
Tan x = 4/ 3
x
4
x = Tan -1 (4/3)
x = 53.13°
x = 53°
6.
Cos x = 10 / 15
15
x = cos -1 (10 / 15)
x
10
x = 48.189°
x = 48°
7.
x
2
Sin x = 2 / 12
x = sin -1 (2 / 12)
12
x = 9.6 °
x = 10 °
8.
Tan x = 5 / 12
5
x = Tan-1 (5/12)
x
12
x = 22.61°
x = 23°
Homework:
p.529(22-26 even,32-36 even,37-43)
p.538(20,30-35)