an airplane leaves an airport and travels 100 miles in a direction of 300 degrees. How far North of the airport is the plane then?
hatdog
To determine how far North of the airport the plane is, we can break down the motion of the plane into its northward and eastward components.
Since the plane is traveling at a bearing of 300 degrees, we need to find the northward component (or the component in the direction of the y-axis) by finding the sine of the angle.
To do this, we can use the formula:
northward component = distance * sin(angle)
In this case, the distance traveled is 100 miles and the angle is 300 degrees. However, it's important to note that the sine function in most programming languages expects the angle to be in radians, not degrees. So we need to first convert 300 degrees to radians.
To convert degrees to radians, we can use the formula:
radians = degrees * π / 180
Using this formula, we can convert 300 degrees to radians:
radians = 300 * π / 180
Now we can calculate the northward component:
northward component = 100 * sin(radians)
To find the value of sin(radians), you can use a calculator or a programming language that has a sine function.