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Solution of Triangles SINE RULE

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22 angle dan 1 side are given e.g A = 60 , B = 40 and side b = 8 cm then, side a & side c can be found using sine rule; B A C a b c 8cm 60 40 1 2 =10.78=12.26 80° How much is angle C?

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SINE RULE → 2 sides and 1 non-included angle given. example; a= 8, b= 10cm and B=70 then we can find A, C and side c using sine rule. B A C a b c 8 cm 10 cm 70° C = 180° - 70° - 48°45’ = 61° 15’ = 9.33 cm

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Practice 1 Find (a) length AC (b) length BC AC = 8.249 cm A = 180 – 45 – 59 = 76 BC = 11.32 cm

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Ambiguous What does am-big-u-ous mean? 1. Open to more than one interpretation 2. Doubtful or Uncertain. Ambiguous indicates the presence of two or more possible meanings.

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Ambiguous Case When length of 2 sides and one non-included acute angle are given, e.g A, side c and a. Þ2Þ2 possible triangle can be drawn: ABC or ABC’ where BC = BC’ A B C C’ c a a

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Example ABC is a triangle with A = 28 , AB = 14 cm and BC = 9 cm. Solve the triangle. 2 possible triangle can be formed. There are 2 possible solution for each sides and angle to be solved. C’ A B C 14 cm9 cm 28 9 cm

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A B C 14 cm9 cm C’ 28 9 cm Example C = sin -1 0,7303 = 46 55’ or 133 5’ ACB = 46 55’ AC’B = 133 5’ ABC = 180 – 28 – 46 55’ = 105 5’ ABC’ = 180 – 28 – 133 5’ = 18 55’ AC = 18.51 AC = 6.215

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Exercise (Ambiguous case) Given a triangle ABC, the length of AB = 8 cm, BC = 7 cm, and A = 48°. Find B, C and the length of AC Answer: B = 73°52’, 10° 8’ C = 58°8’,121° 52’ AC = 9.04 cm, 1.66 cm

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Why does the line y = x only have one slope? What is true about all of the triangles? How does this relate to Pythagorean Theorem?

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