a ship sails 27km due south then 16km due west. How far is the ship to the nearest 0.1 km ,from its starting point?
Use the Pythagorean theorem to find the hypotenuse of this right-angle triangle.
a^2 + b^2 = c^2
27^2 + 16^2 = c^2
729 + 256 = c^2
985 = c^2
31.384 = 31.4 km = c
thanx xx
You're welcome.
To find the distance of the ship from its starting point, we can use the Pythagorean theorem. The Pythagorean theorem 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.
In this case, the ship has sailed 27km due south and 16km due west. We can consider these distances as the lengths of the sides of a right-angled triangle. The side opposite the right angle would be the shortest distance from the ship's starting point to its current location.
Let's label the sides of the triangle:
- The side opposite the right angle (hypotenuse) is the shortest distance from the ship's starting point.
- The side representing the north-south displacement is 27km.
- The side representing the east-west displacement is 16km.
Now we can apply the Pythagorean theorem to find the length of the hypotenuse:
hypotenuse^2 = (north-south displacement)^2 + (east-west displacement)^2
hypotenuse^2 = 27km^2 + 16km^2
hypotenuse^2 = 729km^2 + 256km^2
hypotenuse^2 = 985km^2
Taking the square root of both sides to solve for the hypotenuse:
hypotenuse ≈ √985 ≈ 31.4km
Therefore, the ship is approximately 31.4 km away from its starting point to the nearest 0.1 km.