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6.1 Law of Sines

6.1 Law of Sines. +Be able to apply law of sines to find missing sides and angles +Be able to determine ambiguous cases. Oblique Triangles. A is acute. A is obtuse. B. B. c. a. a. c. A. C. b. C. A. b. Solving Oblique Triangles.

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6.1 Law of Sines

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  1. 6.1 Law of Sines +Be able to apply law of sines to find missing sides and angles +Be able to determine ambiguous cases

  2. Oblique Triangles A is acute A is obtuse B B c a a c A C b C A b

  3. Solving Oblique Triangles • To solve oblique triangles you need one of the following cases • 2 angles and any side (AAS or ASA) • 2 sides and the angle opposite one of them (SSA) • 3 sides (SSS) • 2 sides and their included angle (SAS)

  4. Law of Sines • If ABC is a triangle with sides a, b, and c, then

  5. Example • Find the missing sides and angles given the following information • C = 102.30 • B = 28.70 • b = 27.4 ft

  6. Word Problem • A pole tilts towards the sun at an 80 angle from the vertical, and it casts a 22 foot shadow. The angle of elevation from the tip of the shadow to the top of the pole is 430. How tall is the pole?

  7. Ambiguous Cases (SSA)(h = bsinA) • A is acute • a < h • no triangles • A is acute • a = h • 1 triangle a b b h a h A A

  8. More Cases • A is acute • a > b • 1 triangle • A is acute • h < a < b • 2 triangles b b a a a h h A A

  9. More Cases • A is obtuse • a < b • no triangles • A is obtuse • a > b • 1 triangle a a b b A A

  10. Example • Find the missing sides and angles of the triangle given the following information • a = 22 in • b = 12 in • A = 420

  11. Determine how many triangles there would be? • A = 620 , a = 10, b = 12 • A = 980 , a = 10, b = 3 • A = 540 , a = 7, b = 10

  12. Finding two solutions • Find two triangles for which a = 12, b = 31, and A = 20.50

  13. Example • Find the missing sides and angles for the following information • a = 29 • b = 46 • A = 310

  14. Using Sine To Find Area • Area of an Oblique Triangle

  15. Find the Area of the Triangle • Find the area of a triangular lot having two sides of lengths 90 meters and 52 meters and an included angle of 102o.

  16. Word Problem • The course for a boat race starts at point A and proceeds in the direction S 52o W to point B, then in the direction S 40o E to point C, and finally back to point A. Point C lies 8 kilometers directly south of point A. Approximate the total distance of the race course.

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