Question

A ship is located 40 mi from a straight shoreline. LORAN stations A and B are located on the shoreline, 300 mi apart. From the LORAN signals, the captain determines that his ship is 80 mi closer to A than to B. Find the location of the ship. (Place A and B on the y-axis with the x-axis halfway between them. Find the x - and y-coordinates of the ship.)

Answer 1

The ship is located approximately at coordinates (48.37, 38.41) using the given information.

Step-by-step explanation:

To find the location of the ship, we can set up a coordinate system where point A is at (0, 0) and point B is at (0, 300).

Given that the ship is 80 mi closer to A than to B, we can represent the location of the ship as (x, y), where y is 40 mi from the shoreline and x is 80 mi closer to A than to B.

Using the distance formula, we can set up two equations:

(x-0)^2 + (y-0)^2

= (40)^2 and (x-80)^2 + (y-0)^2

= (300)^2.

Solving these equations, we find that x = 48.37 mi and y = 38.41 mi.

Therefore, the location of the ship is approximately (48.37, 38.41).