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Published byCody Watson Modified over 3 years ago

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The area of an oblique triangle can be found by using the following formula: Ar ea = 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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Find the area of each triangle described below. 1) A = 36 o, b = 3 feet, c = 5 feet Area = ½ bc sinA = ½ ab sinC = ½ ac sinB

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2) C = 100 o, 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 (non right) 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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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

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Use the law of cosines to find the missing sides and angles. A C B a a 2 =b 2 +c 2 -2bc cosA b 2 =a 2 +c 2 -2ac cosB c 2 =a 2 +b 2 -2ab cosC

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Use the law of cosines to find the missing sides and angles. A C B a 2 =b 2 +c 2 -2bc cosA b 2 =a 2 +c 2 -2ac cosB c 2 =a 2 +b 2 -2ab cosC

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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 peri meter, p, of the triangle, p = a + b + c. Area = 1/4 p(p-2a)(p-2b)(p-2c)

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Recap! Draw and label triangle. Decide which law to use base on similarity theorem. AAS ASA SSA SASSSS use law of sines to find missing measures 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 Find Area

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