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Section 9.2

Section 9.2. The Law of Sines. β. a. c. γ. α. b. THE LAW OF SINES. or. WHEN TO USE THE LAW OF SINES. (a) an angle-side-angle (ASA) triangle; an angle-angle-side (AAS) triangle; or a side-side-angle (SSA) triangle. The Law of Sines is used when you have:. SSA TRIANGLES.

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Section 9.2

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  1. Section 9.2 The Law of Sines

  2. β a c γ α b THE LAW OF SINES or

  3. WHEN TO USE THE LAW OF SINES (a) an angle-side-angle (ASA) triangle; • an angle-angle-side (AAS) triangle; or • a side-side-angle (SSA) triangle. The Law of Sines is used when you have:

  4. SSA TRIANGLES Given α, a, b of a triangle. • There is only one triangle if α > 90° or if a > b. • There is no triangle if a is much less than c and α is “too big.” • There are two triangles if a < c and α is “small enough.” (You can check this by seeing if the sum of the given angle and the angle you found is less than 180°.)

  5. EXAMPLE A 47-foot long ladder is positioned 15 feet from the base of a wall that is 11° from vertical as shown in the diagram. How far up the wall does the ladder reach?

  6. HEADING AND BEARING In navigation and surveying, the angular direction in which a craft is traveling is called the heading. Heading is always expressed in terms of an angle measured clockwise from north. The angular direction used to locate one object in relation to another object is called the bearing. Bearing is expressed in terms of an acute angle formed by a north-south line. For example: S 53° E.

  7. EXAMPLE A navigator on a ship sights a lighthouse at a bearing of N36°E. After traveling 8.0 miles with a heading of 332°, the navigator sights the lighthouse at a bearing of S82°E. How far is the ship from the lighthouse at the second sighting?

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