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Understanding Right Triangle Trigonometry: Labeling Sides and Solving for X

This lesson covers the fundamentals of right triangle trigonometry, including the identification of the hypotenuse, opposite, and adjacent sides based on the angle of perspective. Students will learn how to label the sides of a right triangle and apply trigonometric ratios (sine, cosine, and tangent) to solve for unknowns. The example provided illustrates the procedure for marking the angle, labeling the sides, and solving for a variable using the sine ratio. By mastering these concepts, students can effectively tackle problems involving right triangles.

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Understanding Right Triangle Trigonometry: Labeling Sides and Solving for X

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  1. Lesson 7-5 Right Triangle Trigonometry Lesson 7-5 Right Triangle Trigonometry

  2. In right triangles : • The segment across from the right angle ( ) is labeled the hypotenuse “Hyp.”. • The “angle of perspective” determines how to label the sides. • Segment opposite from the Angle of Perspective( ) is labeled “Opp.” • Segment adjacent to (next to) the Angle of Perspective ( ) is labeled “Adj.”. * The angle of Perspective is never the right angle. Hyp. Opp. Angle of Perspective Adj. Lesson 7-5 Right Triangle Trigonometry

  3. Labeling sides depends on the Angle of Perspective If is the Angle of Perspective then …… Angle of Perspective Hyp. Adj. Opp. *”Opp.” means segment opposite from Angle of Perspective “Adj.” means segment adjacent from Angle of Perspective Lesson 7-5 Right Triangle Trigonometry

  4. If the Angle of Perspective is then then Hyp Adj Hyp Opp Opp Adj Lesson 7-5 Right Triangle Trigonometry

  5. Trigonometry Ratios If is the Angle of Perspective then …... Sin = Cos = tan = Hyp Opp Adj Angle of Perspective Lesson 7-5 Right Triangle Trigonometry

  6. Example: Find the value of x. Step 1: Mark the “Angle of Perspective”. Step 2: Label the sides (Hyp / Opp / Adj). Step 3: Select a trigonometry ratio (sin/ cos / tan). Sin = Step 4: Substitute the values into the equation. Sin 25 = Step 5: Solve the equation : Change Sin 25 into a decimal. Cross multiply and solve. Hyp opp Angle of Perspective Adj x = (0.4226) (12) x = 5.07 cm = Lesson 7-5 Right Triangle Trigonometry

  7. Solving Trigonometric Equations There are only three possibilities for the placement of the variable ‘x”. Sin = Sin = Sin = Sin 25 = Sin = Sin 25 = 0.4226 = Sin = 0.48 0.4226 = X = Sin (0.48) x = x = (12) (0.4226) x = 5.04 cm X = 28.6854 x = 28.4 cm Lesson 7-5 Right Triangle Trigonometry

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