Question 18

Explanation

Problem Visualization

Here is an illustration of the eagle and fish positions based on the problem information:

Identify Variables

Given:

• Depth of fish from water surface ($y_1$) = $3 \text{ m}$.
• Total line of sight distance (Eagle to Fish) = $18 \text{ m}$.
• Angle between line of sight and water surface = $30^\circ$.

Let:

• $r_1$ = line of sight distance from fish to the water surface point.
• $r_2$ = line of sight distance from eagle to the water surface point.
• $y_2$ = height of eagle from water surface.

Calculate Fish to Surface Distance

Consider the right triangle formed by the fish's position and the water surface. Using the sine concept:

Calculate Eagle to Surface Distance

The total line of sight distance is the sum of the distance from the fish to the surface and the distance from the eagle to the surface:

Calculate Eagle Height

Now consider the right triangle formed by the eagle's position and the water surface. Again, use the sine concept:

Thus, the height of the eagle above the river surface is $6 \text{ m}$.