After flying 240 miles and being 25 miles off course, what total correction is needed over 100 miles to converge on the destination?

To determine the total correction needed to converge on the destination after flying 240 miles while being 25 miles off course, we can utilize a basic understanding of navigation and trigonometry.

The problem can be visualized as a right triangle, where the 240 miles represents the hypotenuse, the 25 miles represents the perpendicular distance from the intended course to the actual flight path, and the desired correction forms the angle needed to adjust the flight path towards the destination.

To find the angle of correction, we can apply the tangent function from trigonometry, where the tangent of the angle is equal to the opposite side (25 miles) divided by the adjacent side (the distance flown towards the destination). Since you need to correct over the next 100 miles, we can set up the calculation based on the concept that the angle will change with distance travelled.

Using the formula for the angle in a right triangle:

[ \tan(\theta) = \frac{opposite}{adjacent} ]

where:

• The opposite side is 25 miles,

• The adjacent side is 100 miles (the next leg of the journey).

To find the angle in degrees:

1. Calculate the tangent ratio:

[ \tan(\theta