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Oblique Triangles

Oblique Triangles. Oblique Triangle – a non-right triangle. It may be acute. It may be obtuse. All triangles have six parts…three sides and three angles. We will label all our triangles the same way. A. c. b. B. a. C. Law of Sines Used when you have an angle/side pair. B. c. a. A.

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Oblique Triangles

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  1. Oblique Triangles

  2. Oblique Triangle – a non-right triangle. It may be acute. It may be obtuse.

  3. All triangles have six parts…three sides and three angles. We will label all our triangles the same way.

  4. A c b B a C

  5. Law of Sines Used when you have an angle/side pair.

  6. B c a A C b Law of Sines c sin C a sin A b sin B = =

  7. Solve the following triangle: C = 102.3, B = 28.7, and b = 27.4 feet Step 1: Determine whether or not you have a angle/side pair. Step 2: Determine which Law to use. C 102.3 B 28.7 27.4 Step 3: Determine the missing parts. To find A: A = 180 – B – C To find c: b = c sin B sin C b sin B c sin C = A A = 180 – 102.3 – 28.7 A = 49 27.4 = c sin 28.7 sin 102.3 c  sin 28.7 = 27.4  sin 102.3 c = 27.4  sin 102.3 sin 28.7 c = 55.75 feet

  8. C = 102.3, B = 28.7, and b = 27.4 feet 102.3 A = 49 c = 55.75 feet 28.7 C 27.4 B To find a: a = b sin A sin B A a  sin 28.7 = 27.4  sin 49 a = 27.4 sin 49 sin 28.7 a = 43.06 feet a = 27.4  sin 49 sin 28.7

  9. A = 25, B = 35 , a = 3.5 Solve the Triangle.

  10. A pole tilts away from the sun at an 8 angle from 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 43. How tall is the pole? Step 1: Determine the Type of Triangle. Step 2: Determine what part of the triangle you need to find. Step 3: Determine which Law to use. Law of Sines x 8 82 43 22 feet Determine the height of the pole…

  11. Law of Cosines Used when you do NOT have an angle/side pair.

  12. B c a A C b Law of Cosines a2=b2+c2-2bc cosA b2=a2+c2-2ac cosB c2=a2+b2-2ab cosC

  13. Solve the triangle: A = 40, b = 3 and c = 4

  14. Solve the triangle: a = 3, b = 5 and c = 7

  15. A ship travels 60 miles due east, then adjust its course northward. After traveling 80 miles in that direction, the ship is 139 miles from the point of departure. Find the bearing from port to it’s new location.

  16. Summary If the triangle has an angle/side matching pair, use the: Law of Sines If the triangle has an angle/side matching pair, use the: Law of Cosines

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