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**Right Triangle Trigonometry**

Chapter 13 Right Triangle Trigonometry

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**§13.1 – Trigonometric Ratios**

Angle Initial side Terminal side Vertex

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**§13.1 – Trigonometric Ratios**

Measurement Tools - Protractor

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**§13.1 – Trigonometric Ratios**

Types of angles Obtuse Greater than 90° Acute Less than 90° Right Exactly 90°

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**§13.1 – Trigonometric Ratios**

Pythagorean Theorem (Right triangles) c2 = a2 + b2

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**§13.1 – Trigonometric Ratios**

Ex: Find c in the diagram below

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**§13.1 – Trigonometric Ratios**

Ex: Find a in the diagram below

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**§13.1 – Trigonometric Ratios**

Relationship between an acute angle of a right triangle and the lengths of its sides sin A = side opposite A hypotenuse cos A = side adjacent to A hypotenuse tan A = side opposite A side adjacent to A

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**§13.1 – Trigonometric Ratios**

Ex: Find the 3 trigonometric ratios for A

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**§13.1 – Trigonometric Ratios**

Trigonometric ratios of the other angles Use a calculator Examples: Finding the trig value given the angle Find sin 48° Find tan 37.25° Finding the angle given the trig value Find if cos = Find if tan = 3.421

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**§13.2 – Using Trigonometric Ratios to Find Angles**

Finding the angles of a right-triangle Must be given two sides Must decide which trig ratio to use Problems 13.2 #2, 4, 6 (p. 438)

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**§13.3 – Using Trigonometric Ratios to Find Sides**

Finding the sides of a right-triangle Must be given one sides and one acute angle Must decide which trig ratio to use Problems 13.3 #2, 4, 6 (p. 440)

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**§13.4 – Solving Right Triangles**

Solving a triangle – Finding unknown values of sides or angles Tools needed to solve triangles Pythagorean theorem Complementary angles add to 90° Trigonometric ratios Problems 13.4 #2, 4, 6 (p. 442)

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**§13.5 – Applications Involving Trigonometric Ratios**

Problem solving approach Read through problem to be sure you understand what is being asked Draw a diagram to help visualize the situation Look for right triangles Apply trigonometric concepts to solve the problem Problems 13.5 #4, 8 (p. 445)

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