Two boats start their journey from the same point a and travel along directions ac and ad, as shown below: what is the distance, cd, between the boats? 461.9 ft 530.9 ft 646.4 ft 325.5 ft

  461.9 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that ...

  Tan = Opposite/Adjacent

In the diagram, you are given angles and the side opposite those angles. You want to find the difference between the lengths of the adjacent sides.

Solving the above equation for "Adjacent", we get ...

  Adjacent = Opposite/Tan

For our two boats, this tells us ...

  BC = (400 ft)/tan(60°)

  BD = (400 ft)/tan(30°)

Then the difference BD -BC = CD is ...

  CD = BD -BC = (400 ft)/tan(30°) -(400 ft)/tan(60°)

  CD = (400 ft)(1/tan(30°) -1/tan(60°)) ≈ 461.9 ft

Comment on the solution

Of course, 1/tan(x) = cot(x) = tan(90° -x). So, our expression could be ...

  CD = (400 ft)(tan(60°) -tan(30°)) . . . . . a little easier to evaluate

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