Airplane Distance Calculation

How far from the airport is the airplane?

An airplane flies in a straight line from an airport for a distance of 80 miles, turns 15 degrees, and flies in another straight line for a distance of 95 miles. To the nearest mile, how far from the airport is the airplane?

Final Answer:

To calculate the distance from the airplane to the airport, we can use the law of sines and trigonometry. By setting up an equation using the given angle and distances, we can solve for the unknown distance. The airplane is approximately 109 miles away from the airport.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. In this scenario, we are dealing with a triangle formed by the airplane's path from the airport.

The first leg of the triangle is 80 miles long, and after the airplane turns 15 degrees, it flies another 95 miles. We can use the law of sines to calculate the distance from the airplane to the airport.

By setting up the equation sin(15 degrees) / 80 = sin(x) / 95 and solving for x, we find that the airplane is approximately 109 miles away from the airport. This distance can be crucial for navigation and logistics planning.

Understanding trigonometry can help in various real-life situations, such as calculating distances, angles, and heights. It is a powerful tool that is used in many fields, including engineering, physics, and even astronomy.

By mastering trigonometry concepts and formulas, you can solve complex problems like the distance of an airplane from the airport with ease. It is a fascinating branch of mathematics that has practical applications in our daily lives.