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Applications of Trigonometry to Navigation and Surveying

Applications of Trigonometry to Navigation and Surveying. Section 9-5 (day 2). Terminology:. Nautical mile : Unit of linear measure used in navigation About 15% longer than one mile Knot : Unit of speed used by ships and planes 1 knot = I nautical mile per hour 1 knot = 1.15077854 mph.

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Applications of Trigonometry to Navigation and Surveying

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  1. Applications of Trigonometry to Navigation and Surveying Section 9-5 (day 2)

  2. Terminology: • Nautical mile: • Unit of linear measure used in navigation • About 15% longer than one mile • Knot: • Unit of speed used by ships and planes • 1 knot = I nautical mile per hour • 1 knot = 1.15077854 mph

  3. Review: • Law of Cosines: (given SSS, SAS) a2 = b2 + c2 – 2bc cos A • Law of Sines: (given ASA, SAA, SSA) • SAS area formula:

  4. example 1: A ship proceeds on a course of 110 for two hours at a speed of 20 knots, then changes course to 220 for two more hours. How far is the ship from its starting point?

  5. example 2: A ship proceeds on a course of 300° for two hours at a speed of 15 knots, then changes course to 230°, continuing at 15 knots for three more hours. At that time, how far is the ship from its starting point?

  6. example 3: Tower T is 8 km northeast of village V. City C is 4 km from T on a bearing of 150° from T. What is the bearing and distance of C from V?

  7. example 4: A plane flies on a course of 100° at a speed of 1,000 km/hr. How far east of its starting point is it after 3 hours?

  8. example 5: Often a plot of land is taxed according to its area. Sketch the plot of land described, then find its area. From a granite post: • proceed 195 feet east along Tasker Hill Road, • then along a bearing of S32°E for 260 feet, • then along a bearing of S68°W for 385 feet, • finally along a line back to the granite post.

  9. Homework: Page 362 (w) #5 – 7 all 9 – 15 odd (show all diagrams and work)

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