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I encountered the question below on a national-level high school test that took place today.

"Two ships, A and B, depart from the port at the same time. A sails at 8 km/h on a 120 degree course. B sails on a 195 degree course. After 90 min, the course from A to B is 255 degrees. What's the speed of B?

From my point of view the information provided seems scant. We only know that ship A has sailed for 12 km on a course 120 degrees starting from the first quadrant and that after 90 min ship B sails on a course of 15 degrees(not sure on that considering the confusing language of the problem). I was thinking of the cosine theorem but we don't know the distance from A to B. Could you provide some insight on the hidden data and possibly a solution to this problem?

X HOxha
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  • Simple sine rule. The reason you are not seeing the answer, is because you’re failing to see that the third angle is determined by 180 - (sum of the other two angles) in a triangle. – Benjamin Wang Jun 15 '20 at 17:28

1 Answers1

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enter image description here

Like I said in a comment, you’re not seeing the third angle.

It is now a simple application of the sine rule.

Edit: clarification figure

enter image description here

Benjamin Wang
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  • Thank you very much for clarifying it ! Actually I interpreted that "255 degrees" in such a way that after 90 min the ship was sailing at the opposite direction of the beginning (180 degrees away). Therefore I feel compelled to ask you: How does "the course from A to B is 255 degrees" translate into a 45 degrees angle? (I'm unable to demonstrate it with a sketch) – X HOxha Jun 15 '20 at 18:38
  • @XHOxha alright. Please see an additional figure which I will attach as an edit to my answer soon. – Benjamin Wang Jun 16 '20 at 02:59
  • It's all crystal clear now! I had failed to realise that the "255 degrees" angle referred to the one you've shown there ! Yet again thank you – X HOxha Jun 16 '20 at 16:44