A ship leaves port and travels 100 km east. It then turns due south and travels 75 km. How far from the port is the ship?
To find the distance of the ship from the port, we can use the Pythagorean theorem.
Let's say the eastward distance is represented by the letter 'a' and the southward distance is represented by the letter 'b'.
Given that the ship travels 100 km east (a = 100 km) and then turns due south and travels 75 km (b = 75 km), we can find the distance from the port using the formula:
c^2 = a^2 + b^2
where 'c' represents the distance from the port.
Substituting the given values into the formula, we get:
c^2 = (100 km)^2 + (75 km)^2
c^2 = 10000 km^2 + 5625 km^2
c^2 = 15625 km^2
Taking the square root of both sides, we find:
c ≈ √15625 km
c ≈ 125 km
Therefore, the ship is approximately 125 km from the port.
To find the distance of the ship from the port, we can use the Pythagorean theorem.
Step 1: Draw a diagram to visualize the situation. Draw a straight horizontal line to represent the 100 km traveled east, and then draw a straight vertical line to represent the 75 km traveled south. The port is at the starting point.
Step 2: Label the horizontal line as the ship's eastward distance and the vertical line as the ship's southward distance. Thus, the eastward distance is 100 km, and the southward distance is 75 km.
Step 3: Now, let's find the hypotenuse of the right triangle to get the distance from the port. The hypotenuse represents the straight-line distance from the port to the ship's current location.
Step 4: Apply the Pythagorean theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b) of a right triangle.
In this case, a = 100 km (eastward distance) and b = 75 km (southward distance), so we have:
c² = a² + b²
c² = 100² + 75²
Step 5: Calculate the square of each side:
c² = 10000 + 5625
c² = 15625
Step 6: Find the square root of both sides to solve for c:
c = √15625
c ≈ 125
Therefore, the ship is approximately 125 km away from the port.
Did you not make a sketch to see that you are just dealing with a
right-angled triangle?
distance^2 = 100^2 + 75^2
= ....
distance = √(.....)