Question

A Ship leaves port and Sails 35 miles due North and then 20 miles due East. If the ship returns to port by traveling along the diagonal route, how many miles would the ship have sailed altogether?

A. 35
B. 55
C. 20
D. 45

Answer 1

To find the total distance sailed by the ship, one calculates the diagonal distance using the Pythagorean theorem and then adds it to the other two distances. The ship would have sailed a total distance of 95.31 miles.

Step-by-step explanation:

The subject of this question is Mathematics, specifically concerning the topic of geometry and vector addition. The student is asked to calculate the total distance a ship would have sailed after making a trip north, then east, and finally returning to the port along a diagonal route. The first leg of the journey is 35 miles north, and the second leg is 20 miles east. These two segments form a right-angled triangle with the port, the north traveling point, and the east traveling point as vertices.

To find the distance along the diagonal route back to the port, we use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. If we let d represent the diagonal distance, we can express this relationship as:

d2 = 352 + 202

d = √(352 + 202)

d = √(1225 + 400)

d = √(1625)

d = 40.31

Now we can add this distance to the other two legs to get the total distance sailed:

Total distance = 35 + 20 + 40.31

Total distance = 95.31 miles