If a navigation error puts a plane 2 degrees off course, how far off course is the plane after flying 121 miles? Round to the nearest tenth of a mile.
Just explain how to solve, please.
Please
Just draw a diagram (right triangle). The true course is one leg, and the actual course is the hypotenuse. The error is the other leg. So, with an hypotenuse of 121,
error/121 = sin 2°
To solve this problem, you need to use trigonometry. Here's how you can do it step by step:
1. Start by understanding the problem. The navigation error has caused the plane to be 2 degrees off course. This means that the actual course of the plane forms an angle of 2 degrees with the intended course.
2. Next, you need to determine the distance the plane is off course after flying 121 miles. To do this, you'll calculate the lateral (or horizontal) distance between the intended course and the actual course.
3. The trigonometric function that relates the side lengths and angles of a right triangle is the tangent. In this case, the angle of 2 degrees is very small, so we can approximate the tangent of this angle using the small-angle approximation: tangent(angle) = sin(angle) / cos(angle). The small-angle approximation is accurate for small angles measured in radians or degrees.
4. To find the actual distance off course, multiply the distance flown (121 miles) by the tangent of 2 degrees: actual distance off course = 121 miles * tangent(2 degrees).
5. If you're using a calculator, make sure your calculator is set to degrees mode, not radians. Then, enter 2 and calculate the tangent of that angle. Multiply the result by 121 miles.
6. Round your answer to the nearest tenth of a mile to match the required precision.
By following these steps, you can find the distance the plane is off course after flying 121 miles.