This is a engineering question and we are not aloud to use calculus. We are told we have a boat on the bank of a river with a current to the right at 30 mph and the max speed of the boat is 25 mph. The question is, traveling at what angle gives the best chance to make it across? The teacher then went and broke down the idea of it and said he is looking for the angle for the 25 vector relative to the 30 vector that will give the greatest resultant angle. He also stated that when he was first prompted the question that he solved it in a rather long way using calculus but a high school teacher walked up and solved it in a very easy and simple way without calculus. Therefore, I'm assuming it has something to do with triangles but we were given no more information. At first I thought the answer was 135 degrees (45 degrees into the current) based off the knowledge that 45 degrees is the optimal launch angel with gravity but that is not the case here. I tested it, using sin and cos to get the resultant angel to be 55.12 degrees. To check it I then tried 37 and 53 degrees into the current and got 56.3 and 53.16. So 45 degrees into the current cannot be the correct answer. I know it has something to do with it being two vectors of the same degree rather than having something like acceleration in there. From what the teacher said I think there is something from geometry that can be used to solve this without (or maybe just a little) using sin/cos/tan. The resultant will have a greater angle as the y vector approaches equal magnitude as the x vector and will continue to rise as the y is bigger than the x vector, the resultant angle will be even greater. So I know it will be less than 45 but it can't be to low or the height will be lost. Any ideas on how to find the max resultant angle?