a ship which started at port p, sailed 15 km due south to port q , and then a further 20 km due west to port r. calculate pr , the shortest distance of the ship from the port where the journey started .
Use the Pythagorean Theorem to find the hypotenuse of this right triangle.
To calculate the shortest distance of the ship from the port where the journey started, we can use the Pythagorean theorem.
1. Draw a diagram to visualize the problem. Label the starting port as P, the first port visited as Q, and the second port as R. Draw a line between ports P and Q, and another line between ports P and R.
2. Since the ship sailed 15 km due south from P to Q, we can consider the line segment PQ as the ship's southward movement.
3. Similarly, since the ship sailed another 20 km due west from Q to R, we can consider the line segment QR as the ship's westward movement.
4. Now, we can calculate the length of the line segment PR, which represents the shortest distance from port P to the ship's position at port R.
5. Apply the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (PR) is equal to the sum of the squares of the other two sides (PQ and QR).
6. Using the numbers provided, PQ is 15 km and QR is 20 km. Let's calculate PR:
PR^2 = PQ^2 + QR^2
PR^2 = 15^2 + 20^2
PR^2 = 225 + 400
PR^2 = 625
PR = √625
PR = 25 km
Therefore, the shortest distance of the ship from the port where the journey started (PR) is 25 km.