Answer:
The boat is 26 miles far from the dock
Explanation:
The south and west are perpendicular, then The distance from the dock due to south (S) represents a leg of a right triangle, the distance due to west (W)represents the other leg of the right triangle and the distance from the end point of the distance due to west and the dock (D) represents the hypotenuse of the right triangle
By using The Pythagoras Theorem ⇒ (The square of the hypotenuse is equal to the sum of the squares of the other two legs of the right triangle)
∵ D² = S² + W²
∵ A boat leaves the dock and travels 10 miles due south
∴ S = 10 miles
∵ The boat then travels 24 miles due west
∴ W = 24 miles
Substitute the value of S and W in the Pythagoras formula
∴ D² = (10)² + (24)²
∴ D² = 100 + 576
∴ D² = 676
- Take √ for both sides
∴ D = 26 miles
∴ The boat is 26 miles far from the dock