An airplane is approaching Seattle international airport. The pilot begins a 13-degree angle of descent starting from a height of 500 feet. What is the distance (x) from the plane to the airport?
To find the distance (x) from the plane to the airport, we can use the tangent function in trigonometry:
tan(angle) = (opposite side) / (adjacent side)
In this case, the angle (13 degrees) is the angle of descent, the opposite side is the height of the plane (500 feet), and the adjacent side is the distance from the plane to the airport (x), which we are trying to find. Plugging these values into the formula:
tan(13) = 500 / x
To solve for x, we can rearrange the equation:
x = 500 / tan(13)
Now, we can use a calculator to find the value of tan(13) and the value for x:
tan(13) ≈ 0.230868
x ≈ 500 / 0.230868
x ≈ 2164.65
The distance from the plane to the airport is approximately 2,164.65 feet.