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Oblique Triangles

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**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. We will label all our triangles the same way.

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A c b B a C

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

AAS ASA SSA SSS SAS

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**Decide whether the following are ASA, AAS, SSA, SSS, or SAS.**

82 42 cm 65 cm SAS

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**Decide whether the following are ASA, AAS, SSA, SSS, or SAS.**

54 32 mm ASA 37

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**Decide whether the following are ASA, AAS, SSA, SSS, or SAS.**

14 AAS 22 19 miles

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**Decide whether the following are ASA, AAS, SSA, SSS, or SAS.**

65 53 yd SSA 87 yd

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Law of Sines

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

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Law of Sines AAS ASA SSA

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**b sin B = sin C AAS c To find A: A = 180 – B – C To find c: b = c**

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

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**To find a: a = b sin A sin B C = 102.3, B = 28.7, and b = 27.4 feet**

c = feet To find a: a = b sin A sin B a = sin 49 sin 28.7 a sin 28.7 = 27.4 sin 49 a = 27.4 sin 49 sin 28.7 a = feet

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

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**ASA x Law of Sines Determine the height of the pole…**

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

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**Summary Use the Law of Sines Coming Tomorrow….. Law of Cosines**

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

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

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**Find the area of the triangle:**

C = 8430’, a = 16 , and b = 20 Area = 1/2(side)(side) Sin < C A B 8430’ 16 20

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**Law of Cosines a2=b2+c2-2bc cosA b2=a2+c2-2ac cosB c2=a2+b2-2ab cosC a**

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Law of Cosines SSS 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**

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?

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**Summary Use the Law of Sines Use the Law of Cosines If the triangle is**

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

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Using SSS To find Area!!

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**Theorem Heron’s Formula**

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

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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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6.1 Law of Sines Objective To use Law of Sines to solve oblique triangles and to find the areas of oblique triangles.

6.1 Law of Sines Objective To use Law of Sines to solve oblique triangles and to find the areas of oblique triangles.

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