a ship sails due north from port 90 km,than 40 km east and then 70 km north, how far is the ship from port
y distance = 90 + 70 = 160
x distance = 40
want hypotenuse
d = sqrt (40^2 + 160^2)
why sir?? i cant understand why ?
you went a total of 160 straight north
you went 40 east
draw that on a graph, 40 right, 160 up
the angle between north and east is 90 deg
so you want the hypotenuse of that right triangle.
oh i get it thank you
To find the distance of the ship from the port, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ship sails due north for 90 km, then 40 km east, and finally 70 km north. We can consider the distance sailed due north as the first leg of a right-angled triangle, the distance sailed east as the second leg, and the distance between the ship and the port as the hypotenuse.
So, the first leg is 90 km north, the second leg is 40 km east, and we need to find the hypotenuse (the distance between the ship and the port).
Using the Pythagorean theorem, we can calculate the distance between the ship and the port:
Hypotenuse^2 = (first leg)^2 + (second leg)^2
Hypotenuse^2 = 90^2 + 40^2
Hypotenuse^2 = 8100 + 1600
Hypotenuse^2 = 9700
Hypotenuse ≈ √9700
Hypotenuse ≈ 98.49 km
Therefore, the ship is approximately 98.49 km away from the port.