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i know that the triangle ABC that angle A = 32,8 degress ., a is 3,51 and c is 5,72. But there are two posibilities for this triangle? how long are the two sides b?

2007-01-24 09:19:42 · 2 answers · asked by SørenN 1 in Science & Mathematics Other - Science

2 answers

b=3.16 or b=6.46 both to 3 significant figures

2007-01-24 10:01:18 · answer #1 · answered by blaven 1 · 0 0

Use sine rule where A = 32.8°, a = 3.51 and c = 5.72
3.51/ sin 32.8 = 5.72 / sin C
sin C = 5.72sin32.8°/3.51 gives C = 62° or 118°

Use cosine rule with C = 62°:-
B = 85.2°
b² = a ² + c² - 2ac cosB
b² = 5.72² + 3.51² - 2 x 5.72 x 3.51 cos 85.2°
b² = 32.7 + 12.3 - 3.36 = 41.6
b = 6.45

Use cosine rule with C = 118°
B = 29.2°
b² = a² + c² - 2ac cos26.9°
b² = 3.51² + 5.72² - 2 x 3.51 x 5.72 cos 29.2°
b² = 12.3 + 32.7 - 35.1 = 12.9
b = 3.15
Hopefully no numerical errors but method is there giving two values as required.

2007-01-25 07:16:21 · answer #2 · answered by Como 7 · 0 0

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