Angle of Elevation Calculation

The problem describes a scenario involving an aircraft, its height above the ground, and its line of sight distance to a landing point on the airport. This situation can be visualized as a right-angled triangle.

Let's define the parts of this triangle:

• The height of the aircraft above the ground forms the side opposite to the angle of elevation.
• The line of sight distance from the aircraft to the landing point forms the hypotenuse of the triangle.
• The angle of elevation is the angle between the line of sight (hypotenuse) and the horizontal line from the landing point to the point directly below the aircraft.

We are given:

• Height (Opposite side) = 5 km
• Line of sight distance (Hypotenuse) = 10 km

We need to find the angle of elevation, let's call it \(\theta\).

In a right-angled triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse.

So, we can write the relationship as:

\[ \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} \]

Substitute the given values into the equation:

\[ \sin(\theta) = \frac{5 \text{ km}}{10 \text{ km}} \]

Simplify the fraction:

\[ \sin(\theta) = \frac{1}{2} \]

Now, we need to find the angle \(\theta\) whose sine is \(\frac{1}{2}\). This is a standard trigonometric value.

The angle whose sine is \(\frac{1}{2}\) is \(30^\circ\).

Therefore, the angle of elevation is \(30^\circ\).

Comparing this result with the given options, we find that \(30^\circ\) is one of the options.