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Lesson 7-4 Right Triangle Trigonometry Lesson 7-4 Right Triangle Trigonometry 1 In right triangles : The segment across from the right angle ( AC ) is labeled the hypotenuse “Hyp.”. A Hyp. Opp. Angle of Perspective C B Adj. The “angle of perspective” determines how to label the sides. Segment opposite from the Angle of Perspective( AB ) is labeled “Opp.” Segment adjacent to (next to) the Angle of Perspective ( BC ) is labeled “Adj.”. * The angle of Perspective is never the right angle. Lesson 7-4 Right Triangle Trigonometry 2 Labeling sides depends on the Angle of Perspective If A is the Angle of Perspective then …… Angle of Perspective AC Hyp A Hyp. Adj. B Opp. C BC Opp AB Adj *”Opp.” means segment opposite from Angle of Perspective “Adj.” means segment adjacent to the Angle of Perspective Lesson 7-4 Right Triangle Trigonometry 3 If the Angle of Perspective is A then A Hyp C Adj B then A Hyp Opp Opp C B Adj C AC Hyp AC Hyp BC Opp AB Opp AB Adj BC Adj Lesson 7-4 Right Triangle Trigonometry 4 Trigonometry Ratios If C is the Angle of Perspective then …... Sin C = A Opp Hyp Cos C = Adj Hyp tan C = Opp Adj Hyp Opp B Adj C Angle of Perspective Lesson 7-4 Right Triangle Trigonometry 5 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). Opp Sin = Hyp Step 4: Substitute the values into the equation. x Sin 25 = A opp Hyp 12 cm x 25 B 12 Angle of Perspective C Adj Step 5: Solve the equation : Change Sin 25 into a decimal. Cross multiply and solve. 0.4226 = 1 x 12 x = (0.4226) (12) x = 5.07 cm Lesson 7-4 Right Triangle Trigonometry 6 Solving Trigonometric Equations There are only three possibilities for the placement of the variable ‘x”. Sin C = Opp Hyp Sin C = A A 12 cm 25 cm x B Sin xº = C Sin xº = 0.48 x = Sin 1 (0.48) x = 28.6854 25 B Sin 25 = 0.4226 = x 12 1 x 12 Sin C = A x = (12) (0.4226) x = 5.04 cm Lesson 7-4 Right Triangle Trigonometry 25 B C Sin 25 = 0.4226 = 1 x = Opp x x 12 cm 12 cm x 12 25 x Hyp 12 x 12 x 12 0.4226 x = 28.4 cm 7 C 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 8