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Oblique Triangles

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

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

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A a B b C c

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

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

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

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

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

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Law of Sines

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a sin A = b sin B = c sin C a c b A B C

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Law of Sines AAS AAS ASA ASA SSA SSA

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C A B 28.7 102.3 27.4 Solve the following triangle: C = 102.3, B = 28.7, and b = 27.4 feet AAS Step 1: Determine the Type of Triangle. Step 2: Determine which Law to use. b sin B = c sin C Step 3: Determine the missing parts. To find A: A = 180 – B – C A = 180 – 102.3 – 28.7 A = 49 To find c: b = c sin B sin C 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

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

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

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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. ASA 82 8 22 feet 43 Step 2: Determine what part of the triangle you need to find. x Step 3: Determine which Law to use. Law of Sines Determine the height of the pole…

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

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

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

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Law of Cosines a 2 =b 2 +c 2 -2bc cosA b 2 =a 2 +c 2 -2ac cosB c 2 =a 2 +b 2 -2ab cosC a c b A B C

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Law of Cosines SSS SSS SAS SAS

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

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

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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 its new location. The pitchers mound on a womens softball field is 43 feet from home plate and the distance between the bases is 60 feet. How far is the pitchers mound from first base?

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

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Using SSS To find Area!!

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Theorem Herons Formula The area A of a triangle with sides a, b, and c is One more thing…

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

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C3B4ME

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