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 solve the problem, we can use trigonometry.
First, let's draw a diagram:
```
A
|--------x-------|
| / |
| / 13° |
| / |
| / |
| / |
| / 500 ft |
| / |
|/________________|
B
```
In this diagram, A represents the airplane and B represents the airport. x is the distance we want to find.
We know that the angle of descent is 13 degrees, so we can use the tangent function:
```
tan(13) = x / 500
```
To solve for x, we can rearrange the equation:
```
x = 500 * tan(13)
```
Using a calculator, we find that x is approximately 113.6 feet. Therefore, the distance from the plane to the airport is approximately 113.6 feet.
To find the distance (x) from the plane to the airport, we can use trigonometry and the given angle of descent.
First, we need to convert the angle of descent from degrees to radians, as most trigonometric functions take input in radians. To convert degrees to radians, we multiply by π/180.
Angle in radians = 13 degrees × (π/180) ≈ 0.2269 radians
Next, we can use the tangent function (tan) to relate the angle of descent to the distance (x) and the initial height (500 feet). The tangent of an angle is equal to the opposite side divided by the adjacent side.
tan(angle) = opposite/adjacent
Using the given information, we have:
tan(0.2269) = opposite/500 feet
We can solve for the opposite side (x) by rearranging the equation:
x = tan(0.2269) × 500 feet
Now, let's calculate this using a calculator or a programming language that supports trigonometric functions:
x ≈ tan(0.2269) × 500 feet ≈ 48.76 feet
Therefore, the distance (x) from the plane to the airport is approximately 48.76 feet.
To solve this problem, we can use the concept of trigonometry. The given information is an angle of descent of 13 degrees and an initial height of 500 feet. We need to find the distance (x) from the plane to the airport.
We can use the tangent function to find the distance. The tangent of an angle is defined as the ratio of the opposite side length to the adjacent side length. In this case, the opposite side length is the height (500 feet), and the adjacent side length is the distance (x) from the plane to the airport.
Using the tangent function, we have:
tan(13 degrees) = 500 feet / x
To find x, we can rearrange the equation:
x = 500 feet / tan(13 degrees)
Now, we can calculate the value of x using a scientific calculator or an online calculator. Evaluating this expression, we find that x is approximately 2,403.52 feet.
Therefore, the distance from the plane to the airport is approximately 2,403.52 feet.