MTH 112 Elementary Functions Chapter 5 The Trigonometric Functions Section 2 – Applications of Right Triangles.

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Right Triangle Trigonometry

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Presentation transcript:

MTH 112 Elementary Functions Chapter 5 The Trigonometric Functions Section 2 – Applications of Right Triangles

Standard Labeling of Triangles C The right angle is angle C. c b a The sides use the same lower case letter as their opposite angle. A B The acute angles are A and B.

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  H O A SOHCAHTOA  Sin = Opp / Hyp; Cos = Adj / Hyp; Tan = Opp / Adj

“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.

“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.

“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.

“Solving” Right Triangles  Case 3: Given the measure of both acute angles. Not enough information! Why?

Application Problems: Strategy 1. Get to know the problem. a. Read the problem. b. Draw and label a picture or diagram. c. Write down what you know. d. Identify the unknowns (give them names). e. Identify the question.

Application Problems: Strategy 1. Get to know the problem. 2. Find an equation or inequality that relates the known and unknown quantities.

Application Problems: Strategy 1. Get to know the problem. 2. Find an equation or inequality that relates the known and unknown quantities. 3. Solve the equation and state your answer in terms of the problem (i.e. answer the question).

Application Problems: Strategy 1. Get to know the problem. 2. Find an equation or inequality that relates the known and unknown quantities. 3. Solve the equation and state your answer in terms of the problem (i.e. answer the question). 4. Check your answer (i.e. does it make sense in terms of the problem).

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: N25°E or S40°W)  Version 2: Degrees clockwise from north. NOTE: Remember, all of these problems will involve a right triangle.