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.(-4, 0)

Accepted Answer

Welcome back. I am so glad you're here. We're asked to determine the bearing of an object located at the point represented by the coordinates given our given coordinates are negative 12 0. Our answer choices are answer choice. A 270 degrees answer choice B north, 90 degrees west, answer choice C south, 90 degrees west and answer choice D, all of the above. All right, let's first figure out where our object is located on the coordinate system. So we'll draw a vertical Y axis and a horizontal X axis. They come together at the origin in the middle. Now, for the coordinate plane system, we have negative 12 0. For our specific object, we'll always have the X value first followed by the Y value. Our X value here is negative 12. So from the origin, we'll go to the left 12 units and for our Y value of zero from there, we'll go neither up nor down. Now, the scale isn't too important. When we're determining the bearing. We just know that we've got an object located on the negative part of the X axis though we can label it negative 12 0. All right. We recall from previous lessons and from the lessons in the textbook that there are two ways to express bearing. We know that when we're discussing bearing our coordinate system becomes like a compass we have north, which is the positive part of the y axis east, which is the positive part of the X axis at south, which is the negative part of the y axis and west, which is the negative part of the X axis. And for the first way to express bearing, we're always going to start with due north. So our initial side of our angle is going to point do north. So point to the positive part of the y axis. For this way of expressing bearing, we just have an angle measurement. So we're going to move from due north and we're always going to head clockwise and to get to the negative part of the A X axis, which is where that point negative 12 0 is we are going to move from due north all the way around degrees. So our first way to express bearing here is 270 degrees. Now, the other way to express bearing is that we can start with either north or south, so we can start along either of those. And then we are going to head from there east or west, however many degrees we indicate. So we can start first with our initial side heading north. So that one would start with an N for north and then to get to that negative 12 0, we're going to head west 90 degrees. So we say north 90 degrees W or west and that gets us to that point negative 12 0. The other way here, we could start from the south. The south could be our initial side. So we start with an S and then to get to that negative 12 0. This time, we're going to head west again and again, it's 90 degrees. So we have south, 90 degrees west. Now, it's important to note for that type of bearing. We can only start with north or south. We cannot begin with east or west. So there are three acceptable ways to express the bearing for this object. We look at our answer choices and we have the degrees, we have the north 90 degrees west for answer choice. B and then we have the south 90 degrees west for answer choice. C. So answer choice D, all of the above is our correct answer here. Well done. We'll catch you on the next one.

Key Concepts

Bearing

Rectangular Coordinate System

Trigonometric Functions

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