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Nina
Nina asked in Science & MathematicsMathematics · 5 years ago

Can somebody help me solve a problem using Law of Cosines?

A bicycle race follows a triangular course. The three legs of the race are, in order; 2.3km, 5.9km, and 6.2km. Find the angle between the starting line and the finishing line.

The answer I got is 18.23 degrees. Is it correct?

3 Answers

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  • Puzzling
    Lv 7
    5 years ago

    Nope, 71.774°

    Source(s): http://www.calculator.net/triangle-calculator.html...
  • Wayne DeguMan
    Lv 7
    5 years ago

    The 'cosine rule' states:

    a² = b² + c² - 2bcCosA

    Now, the angle is between the 2.3 and 6.2 lines, hence the side opposite is the 5.9.

    i.e. a = 5.9, b = 2.3 and c = 6.2

    so, 5.9² = 2.3² + 6.2² - 2(2.3)(6.2)CosA

    => CosA = (2.3² + 6.2² - 5.9²)/[2(2.3)(6.2)]

    i.e. CosA = 8.92/28.52

    so, A = Cos⁻¹(8.92/28.52) => 71.8°...to 3 s.f.

    :)>

  • Elizabeth M
    Lv 7
    5 years ago

    No, it is 180 -71.77 =108.23 degrees.

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