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Name:
Ms. D’Amato
Date:
Block:
Trigonometric Ratios
The word “trigonometry” means “
.” There are 6
measurements in a triangle:
angle measures and
side lengths. To “solve a triangle”
means to find the unknown angle measures and the unknown side lengths.
Example 1:
Solve ∆ABC.
A
To solve ∆ABC, we need to find the
missing angle and the missing sides:
5
mA = ____°
Example 2:
CB = _____
AB = _____
B
E
Solve ∆GEO.
To solve ∆GEO, we need to find the
missing angle and the missing sides:
mE = _____°
30
C
GE = _____
5 2
GO = _____
G
45°
O
If the triangle is not a special right triangle, we need to know a little trigonometry.
There are 6 ratios in trigonometry. Reminder: ratio means fraction! In geometry we use only 3 of the
trig ratios:

sine (abbreviation is sin)

cosine (abbreviation is cos)

tangent (abbreviation is tan)
pronounced the same as “sign”
(The other 3 ratios are cosecant, secant and cotangent.)
Definitions:
Example 3:
a.)
sine of an acute angle:
opposite leg
hypotenuse
cosine of an acute angle:
adjacent leg
hypotenuse
tangent of an angle:
opposite leg
adjacent leg
Find the missing side length and the trig ratios. If possible, leave your answers in
simplest fraction form.
P
8
Z
R
b.)
10
6
Y
5
X
Q
QR = ______
sin Q = _____
XY = ______
sin Z = ______
cos Q = _____
sin R = _____
cos Y = _____
cos Z = ______
tan Q = _____
tan R = _____
tan Y= _____
tan Z = ______
SohCahToa helps us remember the three trig ratios:
S=
o
h
C=
a
h
T=
o
a
Example 4:
Now let us use Trig Functions to find missing sides!
a.)
Steps:
1. Label the given sides
2. Determine the Trig
Function
3. Set up proportion
4. Solve using crossmultiplication
b.)
c.)
d.)
e.)
Example 5:
Find the area of the triangle below.
Example 6:
Find the perimeter of the triangle below.
Example 7:
Solve for all of the variables.