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1 WARM UP 1)Find the altitude a 1)Find the missing legs. 3) m<1 = 2x + 4 and the m<2= 2x+10. a)Find x if <1 and <2 are complementary b) if they are supplementary

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2 Unit 6-Lesson 2 Right Triangle Trigonometry I can name the sides of right triangle in relation to an acute angle. I can solve for an unknown side of a right triangle using sine, cosine, and tangent.

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3 Remember: Trigonometry – the study of the relationships between the sides and angles of triangles Trigonometric ratio – a comparison of the lengths of two sides of a right triangle

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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. 4 Hyp. Angle of PerspectiveOpp. Adj.

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Labeling sides depends on the Angle of Perspective 5 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

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If the Angle of Perspective is 6 then Opp Hyp Adj then Opp Adj Hyp

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Trigonometry Ratios If is the Angle of Perspective then …... Sin = Cos = tan = 7 Angle of Perspective Opp Hyp Adj

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There is one way used to help remember these ratios: SOHCAHTOA 8 sine cosine tangent O – opposite A – adjacent H - hypotenuse Opposite over hypotenuse

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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 (MAKE SURE CALCULATOR IS IN DEGREE MODE). Cross multiply and solve. 9 Angle of Perspective Hyp opp Adj x = (0.4226) (12) x = 5.07 cm =

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Solving Trigonometric Equations There are only three possibilities for the placement of the variable ‘x”. 10 Sin = We will learn about this tomorrow!!! Sin 25 = x = (12) (0.4226) x = 5.04 cm 0.4226 = Sin 25 = 0.4226 = x = x = 28.4 cm

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11 1. Find sin A. A. B. C. D. 2. Find sin B.

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12 3. Find cos A. A. B. C. D. 4. Find cos B.

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13 5. Find tan A. A. B. C. D. 6. Find tan B.

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Find x. Round to the nearest hundredth if necessary. 14 C 7 x 36° A B OppositeAdjacent Hypotenuse

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Find x. Round to the nearest hundredth if necessary. 15 C 12 x 63° A B Opposite Adjacent Hypotenuse

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16 EXERCISING A fitness trainer sets the incline on a treadmill to 7°. The walking surface is 5 feet long. Approximately how many inches did the trainer raise the end of the treadmill from the floor? Let y be the height of the treadmill from the floor in inches. The length of the treadmill is 5 feet, or 60 inches. Answer: The treadmill is about 7.3 inches high. Multiply each side by 60. Use a calculator to find y. KEYSTROKES: 60 7 7.312160604 ENTERSIN

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17 A.1 in. B.11 in. C.16 in. D.15 in. CONSTRUCTION The bottom of a handicap ramp is 15 feet from the entrance of a building. If the angle of the ramp is about 4.8°, about how high does the ramp rise off the ground to the nearest inch?

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