An aeroplane flies 200km on a bearing of 137 degrees. How far east of its starting point is it?
the plane flies on a heading, not a bearing.
the distance east is 200*sin(90-137) = 200cos(47) = 136.4 km
jijj
To determine how far east the airplane is from its starting point, we need to use trigonometry and the concept of bearings.
First, let's understand what a bearing is. In navigation, a bearing is the direction from one point to another measured clockwise from a reference point. In this case, the bearing of 137 degrees tells us the direction the airplane is flying.
To find how far east the airplane has traveled, we need to break down the given information into its horizontal (east-west) and vertical (north-south) components.
Here's how we can approach this problem step-by-step:
Step 1: Draw a diagram: Sketch a coordinate plane with the starting point as the origin (0,0). Label the east-west direction as the x-axis and the north-south direction as the y-axis.
Step 2: Determine the horizontal and vertical components: Since we want to find the eastward distance, we are interested in the horizontal component of the displacement vector. This component can be found using trigonometry.
The horizontal component can be calculated as follows:
Horizontal component = Distance * cos(Bearing)
Step 3: Plug in the values: Given that the distance traveled is 200km and the bearing is 137 degrees, we can substitute these values into the formula from step 2 to calculate the horizontal component.
Horizontal component = 200km * cos(137 degrees)
Step 4: Calculate the horizontal component: Using a calculator or software, compute the cosine of 137 degrees and multiply it by 200km to find the horizontal component.
Horizontal component ≈ 200km * cos(137 degrees) ≈ -116.20km
Step 5: Interpret the result: The negative value (-116.20km) indicates that the horizontal component of the displacement is directed to the west. Since we want the eastward distance, we take the absolute value and determine that the airplane is approximately 116.20km east of its starting point.
Therefore, the airplane is approximately 116.20km east of its starting point.