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Sine and Cosine Ratios

Sine and Cosine Ratios. (Section 11.5). Firefighter’s dilemma :. Firefighters must quickly determine the highest floor they can reach in a tall building that is on fire. limited by the ladder’s length and the size of the angle the ladder forms with the ground. longest ladder is 100 ft

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Sine and Cosine Ratios

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  1. Sine and Cosine Ratios (Section 11.5)

  2. Firefighter’s dilemma: Firefighters must quickly determine the highest floor they can reach in a tall building that is on fire. • limited by the ladder’s length and the size of the angle the ladder forms with the ground. • longest ladder is 100 ft • largest angle that a ladder can safely make with the ground is 80° (or it will tilt backwards) B ladder 100 ft x A 80° C y ground

  3. Definitions: (two more trig ratios) The sine of an acute angle of a right triangle is the ratio of the length of the opposite leg to the length of the hypotenuse. (solution previous problem using sine) 100ft x (more efficient) 80°

  4. Definitions: (two more trig ratios) The cosine of an acute angle of a right triangle is the ratio of the length of the adjacent leg to the length of the hypotenuse. (solution previous problem using sine) 10° 100ft x (more efficient) 80°

  5. Sine and Cosine: B a c A C b

  6. Trig Acronyms: SOH CAH TOA • SOH (sine opposite overhypotenuse) • CAH (cosine adjacent over hypotenuse) • TOA (tangent opposite over adjacent)

  7. Using trig tables: • Includes trig values for acute angles • All values rounded to thousandths • When using a given trig value to find an angle, use the table value closest to given value, then determine the angle.

  8. Homework: • P456 #1 – 35 43 – 47 54, 55

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