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

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.

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

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.

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

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

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

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

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 =

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 = Sin 25 = = x = x = 28.4 cm

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

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

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

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

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

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: ENTERSIN

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?