Trigonometry

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In an explosion, a piece of debris is tossed 99 meters N 45 W. what is the displacement in the north and west directions. I'm not really sure what it wants when it asks for displacement so I also don't know how to get it.

  • Trigonometry -

    N45W ---> an angle of 135° using trig notation.

    So we are de-composing your vector into its vertical and horizontal displacement.
    horizontal: 99cos 135
    = 99(-√2/2) = appr - 70 metres
    vertical : 99 sin 135° = appr 70 metres

    notice if you construct a right-angled triangle in the 2nd quadrant having an angle of 135° and a hypotenuse of 99 metres, the height can be found:
    h/99 = sin135 ----> h = 99sin135 = appr 70
    the base is :
    b/99 = cos135 ----> b = 99cos 135 = appr -70
    the ordered pair of the end of the hypotenuse is about (-70, 70)

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