This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
The distance between the ship and the boat is approximately 103.3 meters. Here's how to calculate it: 1. Calculate the distance from the tower to the ship (x_ship): Using the tangent function: tan(angle) = opposite / adjacent tan(26.4°) = 75 m / x_ship x_ship = 75 m / tan(26.4°) x_ship = 75 m / 0.4957 x_ship ≈ 151.30 m 2. Calculate the distance from the tower to the boat (x_boat): tan(57.4°) = 75 m / x_boat x_boat = 75 m / tan(57.4°) x_boat = 75 m / 1.5620 x_boat ≈ 48.02 m 3. Calculate the distance between the ship and the boat: Since both are on the same horizontal line from the tower, the distance between them is the difference of their distances from the tower. Distance = x_ship - x_boat Distance = 151.30 m - 48.02 m Distance ≈ 103.28 m Rounding to one decimal place, the distance is 103.3 meters.