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Lesson 9-1 & 9-2: Trigonometry of Right Triangles (Sine, Cosine, Tangent) SOH-CAH-TOA Using Trigonometry in Right Triangles • Be able to find the ________, Opposite ________, Adjacent and __________ sides from an angle Hypotenuse ________ Adjacent Hypotenuse ________ Opposite _______ Opposite ________ Adjacent • __________ & _________ depend on Opposite Adjacent where you start! Next to • Adjacent means “______” STAYS • Hypotenuse ______ hypotenuse Trig Ratios Opposite Adjacent • Use _________, _________, and Hypotenuse ____________ to set up ratios (fractions) • These ratios are related to the size of Angle the__________ • Three Trig Functions Sine (sin) ____________ Cosine (cos) ____________ Find them on your calculator! Tangent (tan) ____________ ALWAYS talking about an angle!!! Sin, cos, tan are _________ Trig Ratios opposite sin hypotenuse adjacent cos hypotenuse opposite tan adjacent ► SOH-CAH-TOA ____________ A 300 2 3 B 1 1 sin sin AA 2 3 2 1 tan tan AA 3 cos cos AA C Using calculator to find angles From the previous slide, solve for angle A: So: 1 sin A 2 1 sin sin A sin 2 1 1 A sin 2 1 1 A 30 1 sin 30 2 0 Inverse of sin is sin-1 sin 1 1 30 0 2 0 angle fraction/decimal Sin of an ___________ gives the ___________________ fraction/decimal angle Sin-1 of an ____________________ gives the ___________ Using Trig • Finding a missing side missing 1. Label the angle, given side, and ___________ side (x) 2. Draw a _____________ stick figure by the angle adjacent 3. Identify the given and missing sides using ___________, ______________, and _________________ opposite hypotenuse SOH-CAH-TOA 4. Choose 1 of the 3 equations from: _________________ 5. Fill in equation with numbers and x proportion (sin, cos, tan can be over “1”) 6. Solve using a __________ • Finding a missing angle given 2 sides 1. Follow steps 1 – 5 above, then inverse 2. Solve for the angle by using the __________ trig function with the fraction/decimal → 5 sin A 8 A sin 1 5 8 Find sin L, cos L, tan L, sin N, cos N, and tan N. Express each ratio as a fraction and as a decimal. Answer: EXERCISING A fitness trainer sets the incline on a treadmill to 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. Proportion: Multiply sin 70 by 60, divide by 1 if you want to KEYSTROKES: SIN 7 X 60 ENTER 7.312160604 Answer: The treadmill is about 7.3 inches high.