Precalculus

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Okay I posted this before but I am still not sure. How would you solve for M?

The resultant of two forces acting on a body has a magnitude of 80 pounds. The angles between the resultant and the forces are 20° and 52°. Find the magnitude of the larger force.

  • Precalculus -

    a and b are forces
    components in direction of resultant --> resultant
    a cos 20 + b cos 52 = 80
    components perpendicular to resultant sum to zero
    a sin 20 = b sin 52

    2 linear equations, two unknowns, solve

  • Precalculus -

    make a sketch to get ∆ABC where ∢B = 20° and ∢A = 52°
    AB is one vector, and AC is your second vector with BC the resultant.
    so ∢C = 108°
    By the sine law
    AB/sin108 = 80/sin52
    AB = 80sin108/sin52 = 96.55 or 97 pounds.

  • Precalculus -

    Question #2
    Which of us is a physicist and which is a mathematician ? :)

  • Precalculus -

    Damon, how would I solve that's what I am confused on

    Reiny, That answer does not fit with any of the given answers

  • Precalculus -

    Ok, let's do that triangle again.
    draw AB the first vector, and AC, the second vector.
    draw AP, the resultant.
    angle BAP = 52
    angle CAP = 20
    AP = 80
    complete the parallelogra BACP, then
    angle APB=20
    angle B = angle C = 108
    AC/sin52 = 80/sin108
    AC = 80sin52/sin108 = 66.3

    (should not have jumped to a triangle too soon)

  • Precalculus -

    Thanks reiny! But one question how do you know when to use the triangle method and when to use parallelogram?

  • Precalculus -

    A good hint is to always draw the parallelogram first with the resultant being the diagonal.
    That way you can use alternate angles (that is where I messed up)
    The diagonal (resultant) will then give you the triangles.
    Depending on the information given, you would then use either the sine law or the cosine law.

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