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

2. 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. Angle of PerspectiveOpp. Adj.

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

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

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

6. 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. Angle of Perspective Hyp opp Adj x = (0.4226) (12) x = 5.07 cm =

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