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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. How you solve the oblique triangle depends on what you are given.

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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. How you solve the oblique triangle depends on what you are given. • AAS • ASA • SSA • SSS • SAS

  6. Decide whether the following are ASA, AAS, SSA, SSS, or SAS. 82 42 cm 65 cm SAS

  7. Decide whether the following are ASA, AAS, SSA, SSS, or SAS. 54 32 mm ASA 37

  8. Decide whether the following are ASA, AAS, SSA, SSS, or SAS. 14 AAS 22 19 miles

  9. Decide whether the following are ASA, AAS, SSA, SSS, or SAS. 65 53 yd SSA 87 yd

  10. Law of Sines

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

  12. Law of Sines • AAS • ASA • SSA

  13. Solve the following triangle: C = 102.3, B = 28.7, and b = 27.4 feet Step 1: Determine the Type of Triangle. Step 2: Determine which Law to use. AAS 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

  14. 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

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

  16. 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 ASA 82 43 22 feet Determine the height of the pole…

  17. Summary If the triangle is AAS ASA SSA Use the Law of Sines Coming Tomorrow….. If the triangle is SAS SSS Law of Cosines

  18. One more thing…. Using SAS To find Area!!

  19. Find the area of the triangle: C = 8430’, a = 16 , and b = 20 Area = 1/2(side)(side) Sin < C 16 8430’ B 20 A

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

  21. Law of Cosines • SSS • SAS

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

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

  24. 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. The pitcher’s mound on a women’s softball field is 43 feet from home plate and the distance between the bases is 60 feet. How far is the pitcher’s mound from first base?

  25. Summary If the triangle is AAS ASA SSA Use the Law of Sines If the triangle is SAS SSS Use the Law of Cosines

  26. Using SSS To find Area!!

  27. One more thing… Theorem Heron’s Formula The area A of a triangle with sides a, b, and c is

  28. Find the area of a triangle whose sides are 5, 8, and 11.

  29. C3B4ME

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