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Unit 7 Part 3
Trigonometry
Sine, Cosine, and Tangent
•Terms
 Comes from two Greek terms
• Trigon meaning triangle
• Metron meaning measure
• Involves triangle measure
• Trigonometry
•Terminology
SOH, CAH, TOA
•
The Sine Ratio is equal to the length of the
Opposite side of the reference angle over the
length of the Hypotenuse.
The Cosine Ratio is equal to the length of the
Adjacent side of the reference angle over the
length of the Hypotenuse.
The Tangent Ratio is equal to the length of
the Opposite side of the reference angle over
the length of the Adjacent side.
•Labeling a Right Triangle
Opposite Side, Adjacent Side, and Hypotenuse
Labeling a right triangle from the reference angle
Note: the right angle is never a reference angle.
. ( Theta )
Hypotenuse
Adjacent
Opposite
•
Sine
=
Opposite Side
Hypotenuse
The Sine Ratio is equal to the length of the Opposite side of the
reference angle over the length of the Hypotenuse
Hypotenuse
Opposite
• Cosine
=
Adjacent Side
Hypotenuse
The Cosine Ratio is equal to the length of the Adjacent side of
the reference angle over the length of the Hypotenuse
Hypotenuse
Adjacent
• Tangent
Opposite Side
= Adjacent Side
The Tangent Ratio is equal to the length of the Opposite side of
the reference angle over the length of the Adjacent Side
Adjacent
Opposite
•
Sine
=
Opposite Side
Hypotenuse
Examples
16
Opposite
Now use your calculator
• Cosine
•
=
Adjacent Side
Hypotenuse
Example
Adjacent
23°
48
K
Now use your calculator
•
Sine
=
Opposite Side
Hypotenuse
Examples
Hypotenuse
17
Now use your calculator
•Tangent
•
Opposite Side
= Adjacent Side
Example
Adjacent
24°
35
R
Opposite
Now use your calculator
• Cosine
=
Adjacent Side
Hypotenuse
Example
Hypotenuse
16
8
Now use your calculator
•Terminology
A quick review
SOH, CAH, TOA
The Sine Ratio is equal to the length of the
Opposite side of the reference angle over the
length of the Hypotenuse.
The Cosine Ratio is equal to the length of the
Adjacent side of the reference angle over the
length of the Hypotenuse.
The Tangent Ratio is equal to the length of
the Opposite side of the reference angle over
the length of the Adjacent side.
• Real World Applications
A biologists is recording the height of trees in a state
park. At a point 125 feet from the base of the tree
and using an angle measurement tool the biologists
notes that the angle of elevation is 37 degrees.
Which trig function should the biologist use and
what is the height of the tree?
• Sketch a drawing and label
Angle of Elevation
Is formed with the
horizon and upward.
37°
125 feet
• Real World Applications
Flight control noted a plane was approaching the
airport and the radar verified it was 3 miles away.
The pilot communicated with the tower and stated
the angle of depression of the plane to the runway
was 29 degrees. Which trig function should be used
to calculate the distance from the plane to the
runway.
•Sketch a drawing and label
Angle of depression
is formed with the horizon
and looking downward
3 miles
29°
3 miles