A radar station locates a sinking ship at range 16.0 km and bearing 136° clockwise from north. From the same station, a rescue plane is at horizontal range 19.6 km, 155° clockwise from north, with elevation 2.35 km.
Incomplete.
To solve this problem, we can use trigonometry and three-dimensional coordinate geometry.
First, let's determine the position of the sinking ship. We have the range and bearing from the radar station. Since the range is the distance from the radar station to the ship, and the bearing is the angle clockwise from north, we can visualize this as a polar coordinate system with the radar station as the origin.
Using the range of 16.0 km, we can determine the coordinates of the sinking ship as follows:
x-coordinate = range × sin(bearing) = 16.0 km × sin(136°)
y-coordinate = range × cos(bearing) = 16.0 km × cos(136°)
Next, let's determine the position of the rescue plane. We have the horizontal range, bearing, and elevation. Since the horizontal range is the distance from the radar station to the plane projected on the ground, and the bearing is the angle clockwise from north, we can also visualize this as a polar coordinate system with the radar station as the origin.
Using the horizontal range of 19.6 km, we can determine the coordinates of the rescue plane as follows:
x-coordinate = range × sin(bearing) = 19.6 km × sin(155°)
y-coordinate = range × cos(bearing) = 19.6 km × cos(155°)
For the elevation, Let's add the height to the y-coordinate:
final y-coordinate = y-coordinate + elevation = (19.6 km × cos(155°)) + 2.35 km
Now, we can determine the horizontal distance and the distance in the vertical direction between the sinking ship and the rescue plane using the coordinates we calculated:
Horizontal distance = sqrt((x-coordinate of ship - x-coordinate of plane)^2 + (y-coordinate of ship - y-coordinate of plane)^2)
Vertical distance = (y-coordinate of ship - y-coordinate of plane)
Finally, we have all the necessary information to answer the question.