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Understanding Right Triangle Trigonometry: Labeling Sides and Solving Equations

Learn how to label sides in right triangles using the Angle of Perspective concept, solve trigonometric equations, and apply trigonometry ratios (sin, cos, tan) with examples and the SOHCAHTOA rule.

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Understanding Right Triangle Trigonometry: Labeling Sides and Solving Equations

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  1. Lesson 7-4 Right Triangle Trigonometry Lesson 7-4 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 7-4 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 to the Angle of Perspective Lesson 7-4 Right Triangle Trigonometry

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

  5. Trigonometry Ratios If is the Angle of Perspective then …... Sin = Cos = tan = Hyp Opp Adj Angle of Perspective Lesson 7-4 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 7-4 Right Triangle Trigonometry

  7. Solving Trigonometric Equations There are only three possibilities for the placement of the variable ‘x”. Sin C = Sin C = Sin C = Sin 25 = Sin xº = Sin 25 = 0.4226 = Sin xº = 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 7-4 Right Triangle Trigonometry

  8. Remember “SOHCAHTOA” S – Sine is O – Opposite over H - Hypotenuse C – Cosine is A – Adjacent over H - Hypotenuse T – Tangent is O – Opposite over A - Adjacent Lesson 7-4 Right Triangle Trigonometry

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