The Primary Trigonometric Ratios

The Primary Trigonometric
Ratios
When working with right angle triangles it is helpful to name the sides
of the triangle.
• The names are opposite, adjacent and hypotenuse and are
dependent on the perspective of a given angle or the angle you are
working with.
• The longest side of each right­angled triangle is called
the hypotenuse. It is easily found since it is always the
side across from the right angle.
• The side across the triangle from the given angle is
called the opposite side.
• The side that helps form or is next to, the given
angle is called the adjacent side.
θ
θ
1

0
116°
1
0
1
2
3
4
2
5
6
C
3
8
7
9
4
10
11
5
12
13
1. a) Label the sides of each triangle. The first one is done for you.
b) Use a ruler to measure all three sides of each triangle and
record them in the chart below.
Use your calculator to find the ratios of the sides and record them in
the chart, correct to one decimal places.
15
14
2

Triangle
Hypotenuse
(mm)
Opposite
(mm)
Adjacent
(mm)
Opposite
Hypotenuse
Adjacent
Hypotenuse
Opposite
Adjacent
A 31 16 27 0.5 0.9 0.6
B 29 15 26 0.5 0.9 0.6
C 66 33 57 0.5 0.9 0.6
We have special names for these ratios…
This means that for any triangle with a 30° angle, the ratios are:
sin 30 o = _________ cos 30 o = _________ tan 30 o = _________
We use the term ______________________ to remember this!
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Problem Solving Steps:
Step 1: Draw a diagram if one is not already included, and label the lengths
and angles we know.
Step 2: Label your hypotenuse, adjacent, and opposite sides according to the
angle we are using.
Step 3: Set up a ratio involving the side we want and the side we know.
Step 4: Use your ratio to solve for your unknown.
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Examples:
1. A hydro pole is to be secured to the ground 10 m away with a guy wire
as shown. Using a device known as a clinometer, a person measures
the angle of elevation to the top of the pole to be 30º.
a) What is the height (h) of the hydro pole?
b) What length of wire (L) will be needed?
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2. A surveyor needs to know the height of a cliff. He measures 100 m horizontally out
from the base of the cliff and then looks up and measures the angle to the top of the
cliff to be 65°. How high is the cliff?
h
65°
100 m
6

Solving for an unknown angle:
Eg) Find the measure of θ.
Summary
Opposite
Hypotenuse
Adjacent
Hypotenuse
Opposite
Adjacent
is called the sine of the angle,
is called the cosine of the angle
is called the tangent of the angle.
These three ratios are called the Primary Trigonometric Ratios.
To simplify things, mathematicians, scientists, engineers, and anyone else using trigonometry
use Greek letters like θ (pronounced “theta”) as the angle and write:
In order to remember these ratios, many people just use the term SOH­CAH­TOA.
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Calculating Side Lengths
The Primary Trigonometric Ratios
8

State the three primary trigonometric ratios for the following
13
5
θ
9

Labelling Convention
B
CAPITAL LETTERS:
angles
small letters:
sides
A
C
wkbk pg 15 and 16
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