A plane takes off making a 32° angle with the
ground. After traveling 8 miles along this
flight path, how far away is the plane from the
airport?
To find the distance from the plane to the airport, we can use trigonometry. Specifically, we can use the sine function.
Let's call the distance from the plane to the airport "x." We can set up a right triangle with the angle of 32° and the side opposite the angle being x (the distance from the plane to the airport). The side adjacent to the angle would be the distance traveled along the flight path, which is given as 8 miles.
Now, we can use the sine function to relate the angle and the sides of the right triangle:
sin(32°) = opposite/hypotenuse
Therefore, sin(32°) = x/8.
To solve for x, we can rearrange the equation:
x = 8 * sin(32°).
Using a calculator, we can find that sin(32°) ≈ 0.5299.
Substituting this value back into the equation, we get:
x ≈ 8 * 0.5299,
x ≈ 4.2392.
Therefore, the plane is approximately 4.2392 miles away from the airport.