Applications of trigonometry to navigation and surveying
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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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Applications of trigonometry to navigation and surveying

Applications of Trigonometry to Navigation and Surveying

Section 9-5

(day 2)


Terminology

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


Review

Review:

  • Law of Cosines: (given SSS, SAS)

    a2 = b2 + c2 – 2bc cos A

  • Law of Sines: (given ASA, SAA, SSA)

  • SAS area formula:


Example 1

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?


Example 2

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?


Example 3

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?


Example 4

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?


Example 5

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.


Homework

Homework:

Page 362 (w) #5 – 7 all

9 – 15 odd

(show all diagrams and work)


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