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 Trigonometry

• Advanced Geometry
• Trigonometry
• Lesson 3

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Parts of a Right Triangle
hypotenuse the side of a right triangle
opposite the right angle
acute angle
hypotenuse
adjacent leg
adjacent leg the leg of a right triangle that
is also a side of the given acute angle
opposite leg
opposite leg the leg of a right triangle that
is not also a side of the given acute angle
hypotenuse
opposite leg
acute angle
adjacent leg
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Sine Ratio

Abbreviated sin
hypotenuse
opposite leg
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Cosine Ratio
Abbreviated cos

hypotenuse
adjacent leg
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Tangent Ratio

Abbreviated tan
adjacent leg
opposite leg
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Write the Ratio Problems
Example
Use ?ABC with right angle C to find sin A, cos
A, tan A, sin B, cos B, and tan B. Express each
ratio as a fraction, and as a decimal to the
nearest hundredth.
AB 17, BC 15, and AC 8
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Find the Value Problems
Examples Use a calculator to find each
value. Round to the nearest ten-thousandth.
tan 56º
cos 89º
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Missing Measure Problems
In problems where either an angle OR side
measure is missing, set up a trigonometric ratio
as shown below.

Name of the Trig. Ratio
Angle Measure or variable
Ratio

tan
47

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Examples Find x. Round to the nearest tenth.
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Examples Find x. Round to the nearest tenth.
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Examples Find x. Round to the nearest tenth.
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Example A fitness trainer sets the incline
on a treadmill to 7º. The walking surface
is 5 feet long. Approximately how many
inches did the trainer raise the end of the
treadmill from the floor?
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Example Find x and y. Round to the nearest
tenth.