Let's review the given information before we try to find the distance between the shipyard and the cargo ship at 4:00PM. We know that objects detected by radar are plotted on a coordinate plane where each unit represents 1 mile and that the shipyard is located at (0,0). The radar showed a cargo ship at (0, 15) at 9:00AM and the same ship appeared at (16, 15) at 10:00AM.
Over the course of 1 hour, the cargo ship traveled from (0, 15) to (16, 15). Let's calculate the distance the ship traveled during that hour!
Horizontal:&16- 0=16
Vertical:&15- 15=0
The ship traveled 16 miles in 1 hour. We know that the difference in time between 9:00AM and 4:00PM is 7 hours. Because we are told that the ship is traveling at a constant speed and in a constant direction, this means that ship travels 7 times further than during the first hour.
16* 7 = 112
The ship traveled 112 miles from point (0, 15) to point (112,15) and arrived at 4:00PM. We can add the point to our diagram.
The distance from the shipyard to the cargo ship at 9:00AM is 15 miles and the distance the cargo ship traveled from 9:00AM to 4:00PM is 112 miles. To find the distance between the shipyard and the cargo ship at 4:00PM, we will draw a triangle with vertices at (0,0), (0,15), and (112,15).
The distance between the shipyard at point (0,0) and the cargo ship at (112,15) is the hypotenuse of the right triangle. We can use the Pythagorean Theorem to find this distance.
a^2+b^2=c^2
In the formula, a and b are the legs and c is the hypotenuse of a right triangle. We will now identify a, b, and c on the diagram.
