Lesson 8-5/8-6

1. Lesson 8-5/8-6 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 Perspective Opp. Adj.

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

4. If the Angle of Perspective is then then Hyp Adj Hyp Opp Opp Adj

5. Trigonometry Ratios If is the Angle of Perspective then …... Sin = Cos = Tan = Hyp Opp Adj Angle of Perspective

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 =

7. Tangent Ratios • Remember, tangent is equal to • So, tan A = • And, tan B =

8. Tangent cont… • To find the angles we need to use the inverse function. • Tan-1 of 8/15 =28.072 is angle A • Tan-1 of 15/8 = 61.927 is angle B • Notice that these two angle measures add up to 90 degrees.

9. 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