You have the boat velocities wrong. That does not matter if you use the Law Of Cosines. If you try to solve this with the Law If Sines by noticing that the other angles are 63 and 180-135=45, you get two different and incorrect answers that do not match the Law Of Cosines answer. If you draw the angles of the two boats to scale, you will see that the boat going 63 deg has a greater horizontal component than the boat going 135 degrees. sin(63) > sin(135). So, the boat going at 63 has less distance to travel than the boat going at 135. Therefore, the 63 boat only needs to go 32km to get to the North line, while the other boat has to go 40km. With this correction, the student can solve the problem with both Law of Cosines and Law of Sines and verify that they get the same answer.
I'm Davis Makabira Kangayia from Kenya. Thank you for the presentation as requested
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You have the boat velocities wrong. That does not matter if you use the Law Of Cosines. If you try to solve this with the Law If Sines by noticing that the other angles are 63 and 180-135=45, you get two different and incorrect answers that do not match the Law Of Cosines answer.
If you draw the angles of the two boats to scale, you will see that the boat going 63 deg has a greater horizontal component than the boat going 135 degrees. sin(63) > sin(135). So, the boat going at 63 has less distance to travel than the boat going at 135. Therefore, the 63 boat only needs to go 32km to get to the North line, while the other boat has to go 40km.
With this correction, the student can solve the problem with both Law of Cosines and Law of Sines and verify that they get the same answer.
This is very interesting
Thank you