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    Each of two forces has magnitude X N, and the resultant of the two forces has magnitude 12N. When the magnitude of one of the forces is increased by 70% the magnitude of the resultant of the two forces becomes 21N. Find X and the angle between the two forces

    I know in the second one. One must use 1.7x.

    However, still not sure about how to go about it. Help would be appreciated.
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    Are you provided with a diagram?
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    Nope.
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    (Original post by Deep456)
    Nope.
    It's a puzzle. Have you typed the question EXACTLY as printed. If not can you give the exact wording?
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    (Original post by steve2005)
    It's a puzzle. Have you typed the question EXACTLY as printed. If not can you give the exact wording?
    Well it's from a friend of mine and he says he gave it exactly as it is written.

    We have both establised:

    12² = X² + X² + 2XXcos(theta) = 2X²(1+2cos(theta))

    21² = X² + (1.7X)² + 2X(1.7X)cos(theta) = 2.89X² + 3.4X²cos(theta)

    Now how to solve?
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    I think these are the diagrams. The angle theta is NOT the required angle but when you know this it is easy to get the required angle.

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    (Original post by Deep456)
    Well it's from a friend of mine and he says he gave it exactly as it is written.

    We have both establised:

    12² = X² + X² + 2XXcos(theta) = 2X²(1+2cos(theta))

    21² = X² + (1.7X)² + 2X(1.7X)cos(theta) = 2.89X² + 3.4X²cos(theta)

    Now how to solve?
    Make \cos\theta the subject of both equations and then solve for X then find angle.
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    (Original post by Deep456)
    Well it's from a friend of mine and he says he gave it exactly as it is written.

    We have both establised:

    12² = X² + X² + 2XXcos(theta) = 2X²(1+2cos(theta))

    21² = X² + (1.7X)² + 2X(1.7X)cos(theta) = 2.89X² + 3.4X²cos(theta)

    Now how to solve?
    21² = X² + (1.7X)² + 2X(1.7X)cos(theta) = 2.89X² + 3.4X²cos(theta)

    The bold should be 3.89X²
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    (Original post by Deep456)
    Now how to solve?
    I'm inclined to make the entire "x^2Cos(theta)" term the subject of each, equate the two, and solve the quadratic for "x".
 
 
 
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