Short Answer 
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. In this scenario, a boat traveling east at 8 m/s and a northward current at 5 m/s results in a resultant speed of approximately 9.4 m/s when calculated using the theorem.
Step 1: Understand the Pythagorean Theorem
The Pythagorean theorem is a fundamental principle in geometry that applies to right-angled triangles. It states that the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the lengths of the other two sides. Specifically, for a triangle with sides of length a and b, the relationship is expressed as c² = a² + b², where c is the hypotenuse.
Step 2: Identify the Speeds of the Boat and Current
In this scenario, the boat travels east with a speed of 8 m/s, while the river’s current flows north at 5 m/s. Both speeds are perpendicular to each other, resulting in a composite motion. This means that instead of traveling in a straight line to the east, the boat is influenced by the river, and its path is directed toward the north-east.
Step 3: Calculate the Resultant Speed
To find the resultant speed of the boat, we apply the Pythagorean theorem using the two speeds. By substituting the values into the equation, we calculate:
- c² = a² + b²
- c² = 8² + 5² = 64 + 25 = 89
- c = ‚à ö89 ‚âà 9.4 m/s
Thus, the resultant speed of the boat is approximately 9.4 m/s, combining both its eastward motion and the northward current. For more details, you can refer to the source provided.