MTH 112 Elementary Functions Chapter 5 The Trigonometric Functions

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MTH 112Elementary Functions Chapter 5The
Trigonometric Functions

• Section 2 Applications of Right Triangles

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Standard Labeling of Triangles
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Reminder Definitions of Trigonometric Functions
of Acute Angles of Right Triangles

• Oscar Had
• A Heap
• Of Apples.

• O opposite
• A adjacent
• H hypotenuse
• sin ? O/H
• cos ? A/H
• tan ? O/A

SOHCAHTOA ? Sin Opp / Hyp Cos Adj / Hyp Tan
Opp / Adj
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Solving Right Triangles

• Using given information about the lengths of
  sides and/or measures of angles of a triangle,
  find the lengths of all of the sides and the
  measures of all the angles of the triangle.

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Solving Right Triangles

• Case 1 Given the lengths of two sides.
• Use the Pythagorean Theorem to find the length of
  the third side.
• Use a trig function to find the measure of one of
  the acute angles (?).
• Calculate the measure of the other acute angle
  (90-?).

NOTE If possible, only use the given information
in ALL calculations.
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Solving Right Triangles

• Case 2 Given the length of one side and the
  measure of one acute angle (?).
• Calculate the measure of the other acute angle
  (90-?).
• Use a trig function to find the length of one of
  the other sides.
• Use a trig function to find the length of the
  third side.

NOTE If possible, only use the given information
in ALL calculations.
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Solving Right Triangles

• Case 3 Given the measure of both acute angles.
• Not enough information! Why?

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Application Problems Strategy

• Get to know the problem.
• Read the problem.
• Draw and label a picture or diagram.
• Write down what you know.
• Identify the unknowns (give them names).
• Identify the question.

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Application Problems Strategy

• Get to know the problem.
• Find an equation or inequality that relates the
  known and unknown quantities.

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Application Problems Strategy

• Get to know the problem.
• Find an equation or inequality that relates the
  known and unknown quantities.
• Solve the equation and state your answer in terms
  of the problem (i.e. answer the question).

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Application Problems Strategy

• Get to know the problem.
• Find an equation or inequality that relates the
  known and unknown quantities.
• Solve the equation and state your answer in terms
  of the problem (i.e. answer the question).
• Check your answer (i.e. does it make sense in
  terms of the problem).

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Types of Applications Using the Trig Functions
and Right Triangles

• Distances between objects or places.
• Angles of elevation depression to determine the
  altitude or height of an object.
• Navigation.
• Bearing
• Version 1 Degrees east or west from north or
  south (examples N25E or S40W)
• Version 2 Degrees clockwise from north.

NOTE Remember, all of these problems will
involve a right triangle.