math

Two cyclist left a sports ground at the same time. The first cycled on the bearing of 30 degree and the second cycled on the bearing of 329 degree. After the first cyclist had covered twice as long as the distance covered by the second cyclist, the distance between them was found to be 7km. Find a) the distance between the sport ground and the second cyclist.
b) how far north of the sport ground is the first cyclist.

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asked by ken
  1. the angle between the two cyclists' courses is 30+31 = 61°
    If the first cyclist traveled 2x km, then the 2nd traveled x km.
    So, using the law of cosines,
    x^2 + (2x)^2 - 2*x*2x*cos61° = 7^2

    Now, knowing 2x, the distance north for cyclist #1 is
    2x cos30°

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