A passenger airplane flying at an altitude of 1.8 km starts its final airport approach by descending at an angle of depression of 6°. How far along the ground is the airplane from its landing point
To find out how far along the ground the airplane is from its landing point, we can use trigonometry. Let's break down the given information:
Altitude of the airplane = 1.8 km
Angle of depression = 6°
First, let's calculate the height from the landing point to the airplane. We can use the tangent function:
tan(angle) = opposite/adjacent
Here, the angle is the angle of depression and the opposite side is the altitude of the airplane. Let's calculate the adjacent side:
adjacent = opposite / tan(angle)
adjacent = 1.8 km / tan(6°)
Using a calculator, we get:
adjacent ≈ 18.6 km
Therefore, the distance along the ground from the airplane to its landing point is approximately 18.6 km.
To find the distance along the ground from the landing point of the airplane, we need to use trigonometry and the given information.
Let's first draw a diagram to visualize the situation. Imagine a right-angled triangle with one side representing the altitude of the airplane (1.8 km), another side representing the distance along the ground (which we want to find), and the angle of depression (6°) as the angle between the altitude and the ground distance.
Using the tangent ratio in trigonometry, we have the formula:
tangent(angle) = opposite/adjacent
In this case, the angle is the angle of depression (6°), the opposite side is the altitude (1.8 km), and the adjacent side is the distance along the ground that we want to find.
So, we can rearrange the formula as follows:
distance along the ground = altitude / tangent(angle)
Plugging in the values:
distance along the ground = 1.8 km / tangent(6°)
Now, let's calculate the tangent of 6 degrees:
tangent(6°) ≈ 0.1051
Substituting this value into the formula:
distance along the ground ≈ 1.8 km / 0.1051
Calculating:
distance along the ground ≈ 17.13 km
Therefore, the airplane is approximately 17.13 km along the ground from its landing point.