A boat sails due north from the port 70 km, then 30 km east and then 60 km north. How far is the boat from the port?
well, it wound up 130 north and 30 east.
Now use the Pythagorean Theorem.
To find the distance of the boat from the port, we can use the Pythagorean theorem.
Step 1: Draw a diagram to visualize the boat's path. Let's take the port as the origin (0,0) on a Cartesian plane.
Step 2: From the port, the boat goes 70 km due north. This means it moves 70 km in the positive y-direction, ending up at (0,70).
Step 3: Next, the boat sails 30 km east. This means it moves 30 km in the positive x-direction, ending up at (30,70).
Step 4: Finally, the boat goes 60 km north. It moves another 60 km in the positive y-direction, ending up at (30,130).
Step 5: Now, we can use the Pythagorean theorem to find the distance from the port to the boat's current position. The Pythagorean theorem states that the square of the hypotenuse (the distance we want to find) is equal to the sum of the squares of the other two sides of a right triangle.
In this case, the horizontal distance (x-coordinate) is 30 km, and the vertical distance (y-coordinate) is 130 km. So, we have:
Distance^2 = 30^2 + 130^2
Step 6: Simplifying the equation:
Distance^2 = 900 + 16900
Distance^2 = 17800
Taking the square root of both sides gives us the distance:
Distance ≈ √17800
Distance ≈ 133.43 km
Therefore, the boat is approximately 133.43 km from the port.