A ship sails 300 km due west and then 100 km due south. At the end of this journey, how far is the ship from its starting position?

Step 1: The journey forms a right triangle with legs of 300 km (west) and 100 km (south). The straight-line distance d from start to end is the hypotenuse: d = √(300~km)² + (100~km)² Step 2: Square the distances. (300)² = 90,000; (100)² = 10,000 Step 3: Add the squares. 90,000 + 10,000 = 100,000 Step 4: Take the square root. d = √100,000 = √10,000 × 10 = 100√(10)~km Final answer: 100√(10)~km

A ship sails 300 km due west and then 100 km due south. At the end of this journey, how far is the ship from its starting position?

Step 1: The journey forms a right triangle with legs of 300 km (west) and 100 km (south). The straight-line distance d from start to end is the hypotenuse: d = √(300~km)² + (100~km)² Step 2: Square the distances. (300)² = 90,000; (100)² = 10,000 Step 3: Add the squares. 90,000 + 10,000 = 100,000 Step 4: Take the square root. d = √100,000 = √10,000 × 10 = 100√(10)~km Final answer: 100√(10)~km

Solved: A ship sails 300 km due west and then 100 km due…

d = \sqrt{100{,}000} = \sqrt{10{,}000 \times 10} = 100\sqrt{10}~\text{km}

Final answer: $\boxed{100\sqrt{10}~\text{km}}$

A ship sails 300 km due west and then 100 km due south. At the end of this journey, how far is the ship from its starting position?

Answer

Step-by-step solution

The journey forms a right triangle with legs of 300 km (west) and 100 km (south).

Square the distances.

Add the squares.

Take the square root.

Try one yourself

Still stuck on this one?

More Mathematics Questions