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Two ships leave a port at the same time. One sails at 17km/h on a bearing of 205 degrees. The other sails at 21 km/h on a bearing of 243 degrees. How far apart are the ships after 2 hours?

micheala950831  Mar 28, 2017
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Two ships leave a port at the same time. One sails at 17km/h on a bearing of 205 degrees.

The other sails at 21 km/h on a bearing of 243 degrees.

How far apart are the ships after 2 hours?

After 2 hours:

Let d = the distance

$$\begin{array}{|rcll|} \hline d^2 &=& 42^2 + 34^2 - 2 \cdot 42 \cdot 34 \cdot \cos(243^{\circ}-205^{\circ} ) \\ d^2 &=& 2920 - 2856 \cdot \cos(38^{\circ} ) \\ d^2 &=& 2920 - 2856 \cdot 0.78801075361 \\ d^2 &=& 2920 - 2250.55871230 \\ d^2 &=& 669.441287699 \\ d &=& 25.8735634905\ km \\ \hline \end{array}$$

The distance after 2 hours is 25.874 km

heureka  Mar 28, 2017
edited by heureka  Mar 28, 2017