Concept Check The two methods of expressing bearing can be interp...

Question

Concept Check The two methods of expressing bearing can be interpreted using a rectangular coordinate system. Suppose that an observer for a radar station is located at the origin of a coordinate system. Find the bearing of an airplane located at each point. Express the bearing using both methods.(-3, -3)

Accepted Answer

Hey, everyone in this problem, we're asked to determine the bearing of an object located at the point represented by the coordinates given. OK. So we're looking for a bearing and the coordinates we're given are negative 10, negative 10. Before answer choices. Option A south 45 degrees west, option B west 45 degrees south, option C south, 135 degrees north and option D north degrees east. All right. So looking at our answer choices, we can actually eliminate one right off the bat when we talk about a berry. OK. Recall that a bearing always takes the vertical axis first. OK? So either north or south comes first when describing that angle. OK. So in option B, we have west first. So that's not correct just based off the notation itself and how we label a bearing. OK. So we can eliminate option B before we really even get started here. So now to move forward with the rest of these figuring out which one is right. Let's go ahead and draw our coordinates. So if we have a plane, OK, we have the point negative 10 10, which is gonna be down in quadrant. OK. So this is our point negative 10, negative 10. And what we can do is we can draw kind of a vector from the origin to this point. And we wanna find the angle that this makes. And what we're gonna do is find the angle which we're gonna call alpha to the closest vertical axis. In this case, is gonna be that south. OK. So we have north pointing up east to the right south, downwards west to the left. So let's find alpha. And then we're gonna see if there are any answer choices that match. We may have to do some more work to look at our bearing. So if we break up this little triangle that we have, OK. And we look at angle alpha, what we know is the length of the two sides that are not the hypo. And we know they both have length 10 because this is point negative 10, negative 10. So what we can do is relate them through tangent. OK. And we can say that tangent of this angle alpha is going to be equal to 10 divided by 10. It's the opposite side divided by the adjacent side. Now this tells us that tangent of alpha is just going to be equal to one. And if we're looking for an angle between zero and 90 degrees where tangent of alpha is equal to one, that's gonna be alpha is equal to 45 degrees. All right. So what we found is that angle alpha is 45 degrees. What that means is that if we start in the seventh direction, so and move 45 degrees towards the west. Shit. So s 45 degrees. W we get to our be now looking at our answer choices, this is one of the answer choices. So we don't need to do any more work to convert this to a bearing from the north because this is a correct bearing that we found here. Ok. And so looking at our answer choices, option A is going to be the correct answer. And that's it for this one. Thanks everyone for watching. I hope this video helped see you in the next one.

Key Concepts

Bearing

Rectangular Coordinate System

Trigonometric Functions

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