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### Understanding Trigonometry: Ratios of Sides and Practical Applications ###

This review dives into the fundamentals of trigonometry, focusing on the relationships between the sides of a triangle relative to an angle. Key concepts include identifying adjacent, opposite, and hypotenuse sides in a right triangle and using the sine, cosine, and tangent ratios (SOH, CAH, TOA) to solve problems. Practical examples demonstrate how to apply these concepts to real-world scenarios, such as measuring the height of a tree or calculating distances. Understand how to label triangle sides, choose the right formula, and check your work for accuracy. ###

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### Understanding Trigonometry: Ratios of Sides and Practical Applications ###

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  1. Introduction to TrigonometryPart 2

  2. Review: Adj/ Opp / Hyp • Let b be your reference angle • A is the adjacent side (next to the angle) b C A • B is the opposite side (across from the angle) B b Next • C is always the hypotenuse hyp Longest adj opp Across

  3. But if we switch angles… • Now let a be your reference angle • A is the opposite (across from the angle) C A a • B is the adjacent (next to the angle) B Across • C is always the hypotenuse hyp Longest opp a adj Next

  4. Trigonometry uses ratios of the sides • There are three sets of ratios for any triangle • sin…short for sine • cos…short for cosine • tan…short for tangent

  5. So what are the formulas? Tan is Opposite over Adjacent Sin is Opposite over Hypotenuse Cos is Adjacent over Hypotenuse SOH CAH TOA

  6. Another tangent example • Find side B. b C A = 6 25° B

  7. An application • You look up at an angle of 65° at the top of a tree that is 10m away • the distance to the tree is the adjacent side • the height of the tree is the opposite side 65° 10m

  8. Example 3 • Angle b = 66.4 ° • Side A = 4 cm • Find side C 66.4 ° C = x A = 4 a B

  9. One last example… • Lucretia drops her walkman off the Leaning Tower of Pisa when she visits Italy • It falls to the ground 2 meters from the base of the tower • If the tower is at an angle of 88° to the ground, how far did it fall?

  10. First draw a triangle • What parts do we have? • We have an angle • We have the Adjacent • We need the opposite • Since we are working with the adj and opp, we will use the tan formula B 88° 2m

  11. So lets calculate • Lucretia’s walkman fell 57.27m B 88° 2m

  12. What are the steps for doing one of these questions? • Label the sides • Choose SOH, CAH, or TOA • Solve the equation for the unknown value • Does the answer make sense?

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