A ship sails due north 3 kilometres( Point A) and then due east 16 kilometres(Point B) the returns to its original starting point. How far does it travel from point b back to the start. ( Shortest Distance)
3^2 + 16^2 = c^2
9 + 256 = c^2
265 = c^2
16.28 = c
To find the shortest distance from Point B back to the starting point, we can use the Pythagorean theorem.
First, let's represent the distances sailed to the north, east, and the shortest distance back as legs of a right triangle. The distance sailed to the north (Point A) is 3 kilometers, and the distance sailed to the east (Point B) is 16 kilometers. Now, we need to find the shortest distance back to the start (hypotenuse of the triangle).
Using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, we can calculate the shortest distance back.
Hypotenuse^2 = North Leg^2 + East Leg^2
Let's substitute the values into the formula:
Hypotenuse^2 = 3^2 + 16^2
Hypotenuse^2 = 9 + 256
Hypotenuse^2 = 265
To find the length of the hypotenuse, we take the square root of both sides:
Hypotenuse = √265
Therefore, the ship travels approximately √265 kilometers from Point B back to the starting point, which is approximately 16.28 kilometers (rounded to two decimal places).