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27 April 2012 Geometry

27 April 2012 Geometry. Warm Up Check your Homework- “why did the mural…” HOMEWORK DUE TUESDAY: pg. 645: 1 - 20. Objective. Students will use sine, cosine and tangent ratios to solve problems. Students will take notes and solve problems.

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27 April 2012 Geometry

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  1. 27 April 2012 Geometry Warm Up Check your Homework- “why did the mural…” HOMEWORK DUE TUESDAY: pg. 645: 1 - 20

  2. Objective Students will use sine, cosine and tangent ratios to solve problems. Students will take notes and solve problems.

  3. You are on a boat tour around a tropical island. You see a man at the top of a cliff, diving into the water below. You know that your boat is 500 feet from the base of the cliff (your tour guide tells you) and you estimate that the angle that you look up to the top of the cliff is 30⁰ from horizontal. How high is the cliff?

  4. Right Triangle Vocabulary hypotenuse- the longest side leg adjacent- the side that is not the hypotenuse that helps form the angle; adjacent means “next to” leg opposite- the side that does not help form the angle; side “across” the triangle ANGLE Hypotenuse Adjacent Opposite

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

  6. 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

  7. 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

  8. Solve for x. Round to the nearest 1000th. 1. 2. 3. 4. 5. 6.

  9. How do you know which ratio to use? • Identify H, A and O. • What information do you have? What information do you need to find? • Use the trig ratio with “have/need” sides. DO Handout- TRIG Worksheet 3- Calculating Sides

  10. 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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