How can I solve this?

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3 Answers

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  • Philip
    Lv 6
    1 month ago

    By law of cosines a^2 = b^2 + c^2 - 2bc*cos A.

    b = 2, c = 5rt3, A = 30 deg. rt = ''square root of''.;

    So a^2 = 2^2 + (5rt3)^3 -2*2*5rt3*cos30deg;

    = 79 -20rt3(1/2)rt3)= 79-30 = 49. Then a = 7.;

    Option D. gives correct answer.

  • 1 month ago

    You have two sides and an included angle (30°), so use the Law of Cosines. I'm using the version with a² on the left hand side because you are looking for a.

    a² = b² + c² - 2bc cos A

    A = 30°

    b = 2

    c = 5√3

    Plug in, solve for a², then take the square root.

    a² = 2² + (5√3)² - 2(2)(5√3) cos(30°)

    a² = 4 + (25*3) - 20√3 * √3/2

    a² = 4 + 75 - 20 * 3/2

    a² = 79 - 30

    a² = 49

    a = √49

    a = 7

    Answer:

    D. 7

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