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 ________, ________, and __________ sides from an angle __________ & _________ depend on where you start! Adjacent means “______” Hypotenuse ______ hypotenuse Opposite Adjacent Hypotenuse Adjacent ________ Hypotenuse Hypotenuse Opposite ________ Opposite _______ ________ Adjacent Opposite Adjacent Next to STAYS

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

Trig Ratios A 300 2 B C 1 SOH-CAH-TOA ► ____________

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

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

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

Answer: Example 4-1e

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. Example 4-3a

Proportion: Multiply sin 70 by 60, divide by 1 if you want to KEYSTROKES: 7 60 7.312160604 SIN ENTER X Answer: The treadmill is about 7.3 inches high. Example 4-3b