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22April 2013 Geometry

22April 2013 Geometry. Finish Calculating Ratios from last Friday Warm UP: Find x: 1. x 2. L ║ M 3. Read and highlight “Trigonometry”. 7. 6. L. x. 5. M. 144º.

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22April 2013 Geometry

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  1. 22April 2013 Geometry Finish Calculating Ratios from last Friday Warm UP: Find x: 1. x 2. L║M 3. Read and highlight “Trigonometry” 7 6 L x 5 M 144º

  2. Objective Students will use trig ratios to find missing side lengths in triangles. Students will take notes and work with their group. ACT Testing on April 23- ONLY JUNIORS come to school HOMEWORK DUE TUESDAY midnight Spring Project Proposal DUE Wed/ Thursday “Why did the mural painter…” both sides

  3. Right Triangle Vocabulary hypotenuse- the longest side leg adjacent- “next to” leg opposite- “across” ANGLE Adjacent Hypotenuse Opposite

  4. Activity-Calculating ratios for similar triangles EXPECTATIONS- Take 5 minutes to finish 1. Complete the worksheet writing the ratios as a fraction and decimalfor your two triangles. 2. Share your results with your group- each person filling in their DECIMAL COLUMN for all triangles measuring. 3. Calculate the mean values for each ratio rounding to 2 decimal places.

  5. on a calculator 1. MAKE SURE YOU ARE IN DEGREE MODE mode  arrow to DEGREE  enter  2nd QUIT 2. Try it on your calculator for YOUR angle measure: sin 45⁰ sin 30⁰ sin 60⁰ sin 20⁰ cos 45⁰ cos 30⁰ cos 60⁰ cos 20⁰ tan 45⁰ tan 45⁰ tan 60⁰ tan 20⁰ WHAT DO YOU NOTICE?

  6. the trig functions sine, cosine and tangent are RATIOSof side lengths ofright trianglesSince right triangles with the same acute angle measure are similar(AA Similarity Conjecture)these ratios are PROPORTIONALand their decimals are equivalent,NO MATTER THE SIDE LENGTHS

  7. Sine, Cosine and Tangent are special ratios defined as follows:SOH CAH TOA WRITE THESE DOWN Sine = “sin” ϴ = MEMORIZE THESE!! Cosine = “cos” ϴ = Tangent = “tan” ϴ =

  8. A SKETCH on your paper MARK sides H, A and O Find the ratios: sin A = cos A = tan A = sin B = cos B = tan B = What do you notice? Any patterns? 13 5 12 B

  9. Read Trigonometry Handout HIGHLIGHT / underline or circle key phrases: 1) What does Trig mean? 2) What do we call angle “x”? 3) What happens to adjacent and opposite if the angle changes position? 4) Adjacent means __________ Opposite means ___________ 5) MEMORIZE how? 6) How do you know which ratio to use?

  10. solving equations with trig functions 1) Strategy– rewrite the trig function as a decimal and solve for the unknown value ex:  sin 42⁰ ≈ 0.6691 0.6691 = 20 (0.6691) = x x = 13. 3826

  11. solving equations with trigfunctions 2)– remember sinϴ, cosϴ, tanϴ are RATIOS YOU CAN NOT DIVIDE the angle measure to simplify!!! STRATEGY– use parenthesis to help you remember! 20 (sin 42⁰) = x multiply both sides by 20 20 (0.6691) = x use calculator x = 13.2826

  12. How do you know which trig ratio you need to use to help find “x”? 1) use SOH CAH TOA 2) LABEL H, A and O on your triangle. 3) WHAT information DO YOU KNOW? 4) WHAT DO YOU NEED TO FIND? SOH CAH TOA

  13. practice HOW do you know which function to use? LABEL H, A and O WHAT INFORMATION do you KNOW? WHAT DO YOU NEED TO FIND? Choose the trig function that incorporates those values!! COMPLETE HANDOUT- TRIGONOMETRY first section #1 - 18 Set up and solve for the unknown value.

  14. debrief Why do the trig ratios remain equivalent for any acute angle, no matter how big the triangle? How do you know which trig function to use when solving trig problems?

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