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**Area = ½ bc sinA = ½ ab sinC = ½ ac sinB**

The area of an oblique triangle can be found by using the following
formula: Area = ½ bc sinA = ½ ab sinC = ½ ac sinB Since not all triangles are labeled A,B,C, you should remember
that the AREA of a triangle = 1/2 the product of _________and the sine of ___________.

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**Area = ½ bc sinA = ½ ab sinC = ½ ac sinB**

Find the area of each triangle described below. 1) A = 36o, b = 3 feet, c = 5 feet Area = ½ bc sinA = ½ ab sinC = ½ ac sinB

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**Area = ½ bc sinA = ½ ab sinC = ½ ac sinB**

2) C = 100o, a = 12 inches, b = 10 inches Area = ½ bc sinA = ½ ab sinC = ½ ac sinB

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Continuing our discussion of dealing with oblique (nonright)
triangles, today we will look at the Law of Cosines. Yesterday we talked finished talking about Law of Sines. (Used
with: AAS ASA SSA *check for ambiguous cases! - 0,1, or 2 Triangles Law of Cosines is used for: SAS SSS when there isn't an angle and opposite side pair

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**a2 =b2+c2 -2bc cosA b2 =a2+c2 -2ac cosB c2 =a2+b2 -2ab cosC**

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

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**a2 =b2+c2 -2bc cosA b2 =a2+c2 -2ac cosB c2 =a2+b2 -2ab cosC**

Use the law of cosines to find the missing sides and angles. C a2 =b2+c2 -2bc cosA b2 =a2+c2 -2ac cosB c2 =a2+b2 -2ab cosC 8 a 700 B 6 A

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**a2 =b2+c2 -2bc cosA b2 =a2+c2 -2ac cosB c2 =a2+b2 -2ab cosC**

Use the law of cosines to find the missing sides and angles. C a2 =b2+c2 -2bc cosA b2 =a2+c2 -2ac cosB c2 =a2+b2 -2ab cosC 7 8 A 12 B

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**Area = 1/4 √ p(p-2a)(p-2b)(p-2c)**

Another method for finding the area of a triangle (if we do not know the height) is Heron's Formula,
which is based on the perimeter, p, of the triangle,
p = a + b + c. Area = 1/4 √ p(p-2a)(p-2b)(p-2c)

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**use law of cosines to find an a**

Recap! Draw and label triangle. Decide which law to use base on similarity theorem. AAS ASA SSA SAS SSS check ambiguous cases for how many triangles use law of cosines to find an a missing piece use law of sines to find missing measures use law of sines to find missing measures Find Area

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5.6 Law of Cosines. I. Law of Cosines In any triangle with opposite sides a, b, and c: The Law of Cosines is used to solve any triangle where you are.

5.6 Law of Cosines. I. Law of Cosines In any triangle with opposite sides a, b, and c: The Law of Cosines is used to solve any triangle where you are.

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