A boat leaves the dock and travels 10 miles due south, then 24 miles due west. How far is the boat from the dock?

The boat is 26 miles far from the dock

Step-by-step 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

step-by-step explanation: