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Two harbours p and q are 70 km apart with q bearing 90 degrees from p. ship s bears 50....

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Two harbours p and q are 70 km apart with q bearing 90 degrees from p. ship s bears 50. Degrees from p and 35 degrees from q. How far is s from q?

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`theta_(qps) = 90-50=40 deg`
`theta_(pqs)=90-35=55deg`
`theta_(qsp) = 180-40-55=85 deg`

Using the law of sines:

`sintheta_(qsp)/(pq)=sintheta_(qps)/(qs)`

`sin85/70=sin40/(qs)`

`qs=(70sin40)/sin85=45.2`

Therefore, the ship is 45.2 km from the harbour at q.

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