A ship corved a distance of 41 km due north and them 23 km due east and again 15km towards north direction. How far is it from the point where it started?
distance^2 = (41 + 15)^2 + 23^2
To find the distance from the point where the ship started, we can use the Pythagorean theorem.
1. Start by drawing a diagram to visualize the ship's movements. Let's assume the ship started at the origin (0,0) on a Cartesian coordinate system.
2. The ship traveled 41 km due north, so it ended up at point (0,41).
3. Next, the ship traveled 23 km due east, so its new location is (23,41).
4. Finally, the ship traveled 15 km towards the north direction, bringing it to the point (23,56).
5. Now, we can calculate the distance between the starting point (0,0) and the ending point (23,56) using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
- The horizontal side (base) of the triangle is 23 km.
- The vertical side (height) of the triangle is 56 km.
Applying the Pythagorean theorem, we have:
distance^2 = 23^2 + 56^2
distance^2 = 529 + 3136
distance^2 = 3665
Taking the square root of both sides:
distance = sqrt(3665)
distance ≈ 60.54 km
Therefore, the ship is approximately 60.54 km away from the point where it started.