5.2 Apply the Tangent Ratio

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5.2 Apply the Tangent Ratio

• Pg. 157

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Labeling a Triangle
B
c
a
A
C
b
Vertices are labeled with Upper Case CAPITAL
Letters Sides are labeled with lower case
letters, and correspond to the angle opposite of
the side Remember the sum of all angles in a
triangle is 180 Two angles are complimentary
angles if their sum is 90
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The Tangent Ratio

• Let be a right triangle with acute
  . The tangent of (written as tan A) is
  defined as follows

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Real Life Problem
How tall is the tree if a 6 ft. tall man is 60
ft. from the base and has an angle of elevation
of 37
We will use trigonometry to solve
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Trigonometry

• Trigonometry
• the study of the ___________ of _____________
• Trigonometric Ratio
• the ___________ of ___________ of ____ sides of a
  _____________ triangle.

• To find missing lengths of a right triangle
• Given To Find Use
• 2 sides 1 side Pythagorean Theorem
• 2) 1 side Other 2 sides a) Use Special Right
  Triangle
• IF IT IS ONE!
• b) Use Trig Ratios
• IF IT ISNT SPECIAL!

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Trigonometric ratios are great if youre only
given 2 pieces of information IN ADDITION TO
ALREADY HAVING THE _________
angle.Example 1) 2)
x
37
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Real Life Problem
How tall is the tree if a 6 ft. tall man is 60
ft. from the base and has an angle of elevation
of 37
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Homework

• Pg. 161, 1 20 all

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5.3 Apply the Sine and Cosine Ratios

• Pg. 163

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The Sine and Cosine Ratios

• Let be a right triangle with acute
  . The sine of and the cosine of
  (written as sin A and cos A) is defined as
  follows

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3 Basic Trigonometric Ratios

• Remember, a ratio compares two things.
• We will be comparing 2 ____________
• The reference angle is never _________

Name Abbreviation Need a reference
Sine sin sin ( )
Cosine cos cos ( )
Tangent tan tan ( )
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AGAIN, YOU CANNOT TAKE THE SIN, COS, OR TAN OF
ANYTHING UNLESS YOU HAVE A REFERENCE ANGLE
YOURE USING!
So how do you use these Trigonometric
Ratios? Its all about the relationships Youve
got ________, ________, and _______ sides
with trig ratios.
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SOH CAH - TOA
a 4 b 5 c 3
sin A sin C
cos A cos C
tan A tan C
A
b 5
c 3
C
B
a 4
Why not sin B, cos B, or tan B ?
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Homework

• Pg. 161, 1 20 all