12 – Solving Trig Problems Part1

So let me demonstrate how to solve a problem like this. Here we have a vehicle with a heading of 65 degrees and the displacement of 17 meters. I’m going to show you how I would find out the “x” systematically and the first thing I’m going to do is draw the triangle. Here we have a right triangle with a reference angle of 65 degrees. Next, I’m going to identify the known and unknown sides of the triangle. So, in this case, the known side is the hypotenuse with a length of 17 meters, and the unknown side is this delta x, and that’s the adjacent side. Now I want to find the trigonometric ratio that relates the known and unknown sides. So, in this case, I’m looking for the ratio that relates the hypotenuse to the adjacent. That happens to be the cosine because cosine is adjacent over hypotenuse which, in this case, is delta x over 17. Now, all that’s left to do is do the math. So, the first thing I want to do, now that I’ve cleaned things up on the left over here, is rearrange this equation to get delta x alone. Then, I can use Python or a calculator to look up the cosine of 65 degrees. And remember, you really have to be careful with degrees and radians here. But, once I get the answer, I see the cosine of 65 degrees at 0.423. And now I just do up the multiplication to find that delta x is seven point one eight meters. Now, I want you to try to find the length of the opposite side, delta y. Go slow, be careful with your math and feel free to rewatch this video if you find that helpful. But, try your best to get it right on your first attempt.

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