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Math Help - Triangle problem

  1. #1
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    Triangle problem

    In triangle ABC,AB = 7 cm, BC= 5 cm and AَBC = 136ْ .




    (i) Calculate the lenght of AC.
    (ii) Calculate the area of the triangle ABC.


    plz
    tell me hw to solve these question
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  2. #2
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    Jan 2008
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    Hello! I shall do part (a) first...

    Have you learnt Cosine Rule?
    Basically Cosine Rule states that (in the context of this question):

    AC^2 = AB^2 + BC^2 - 2 (AB)(BC) cos \angle ABC

    Therefore, by applying Cosine Rule, we can find AC:

    AC^2 = (7)^2 + 5^2 - 2 (7)(5) cos 136

    AC = \sqrt{124.35} [rounded off to 5 significant figures] = 11.2 cm [rounded off to 3 significant figures]
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  3. #3
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    Jan 2008
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    Okay now for part (b)...

    The formula for area of triangle is (in the context of the question):

    Area of triangle ABC  = \frac{1}{2} (AB)(BC) sin \angle ABC

    In general, the formula is Area of triangle ABC = \frac{1}{2}ab sin C, where a and b are adjacent sides of a triangle and C is the angle opposite side c (i.e. the angle between sides a and b).

    By applying this formula, we can answer the question:

    Area of triangle ABC =  \frac{1}{2} (7)(5) sin 136 = 12.2 cm^2 (rounded off to 3 significant figures)

    Hope this helps! ^^
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