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Lesson 9-1 & 9-2: Trigonometry of Right Triangles (Sine, Cosine, Tangent) SOH-CAH-TOA

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Using Trigonometry in Right Triangles Be able to find the ________, ________, and __________ sides from an angle __________ & _________ depend on where you start! Adjacent means “______” Hypotenuse ______ hypotenuse ________ Hypotenuse ________ _______ ________ Adjacent Hypotenuse Adjacent Opposite Adjacent Hypotenuse OppositeAdjacent Next to STAYS

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Trig Ratios Use _________, _________, and ____________ to set up ratios (fractions) These ratios are related to the size of the__________ Three Trig Functions ____________ Find them on your calculator! Sin, cos, tan are _________ talking about an angle!!! OppositeAdjacent Hypotenuse Angle Sine (sin) Cosine (cos) Tangent (tan) ALWAYS

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Trig Ratios A BC ► ____________ SOH-CAH-TOA

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Using calculator to find angles From the previous slide, solve for angle A: Inverse of sin is sin -1 So: Sin of an ___________ gives the ___________________ Sin -1 of an ____________________ gives the ___________ angle fraction/decimal

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Using Trig Finding a missing side 1.Label the angle, given side, and ___________ side (x) 2.Draw a _____________ by the angle 3.Identify the given and missing sides using ___________, ______________, and _________________ 4.Choose 1 of the 3 equations from: _________________ 5.Fill in equation with numbers and x 6.Solve using a __________ (sin, cos, tan can be over “1”) Finding a missing angle given 2 sides 1.Follow steps 1 – 5 above, then 2.Solve for the angle by using the __________ trig function with the fraction/decimal → missing stick figure adjacent oppositehypotenuse SOH-CAH-TOA proportion inverse

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Example 4-1a Find sin L, cos L, tan L, sin N, cos N, and tan N. Express each ratio as a fraction and as a decimal.

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Example 4-1e Answer:

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Example 4-3a 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.

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Example 4-3b Proportion: Multiply sin 7 0 by 60, divide by 1 if you want to Answer: The treadmill is about 7.3 inches high. KEYSTROKES: SINENTERX

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