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
Here's the solution for question 9(a)(ii), calculating the distance between the ship and the boat. We assume the ship and boat are on the same side of the tower, with the ship being further away due to its smaller angle of elevation. Step 1: Identify the knowns and set up the trigonometric relationships. Let H be the height of the tower, H = 75 m. Let d_S be the distance from the foot of the tower to the ship. Let d_B be the distance from the foot of the tower to the boat. The angle of elevation from the ship is _S = 26.4^. The angle of elevation from the boat is _B = 57.4^. Using the tangent function for right-angled triangles (() = oppositeadjacent): d_S = (H)/((_S)) d_B = (H)/((_B)) The distance between the ship and the boat is D = d_S - d_B. Step 2: Calculate the distance from the foot of the tower to the ship (d_S). Substitute the values into the formula for d_S: d_S = (75)/((26.4^)) d_S ≈ (75)/(0.495726) d_S ≈ 151.299 m Step 3: Calculate the distance from the foot of the tower to the boat (d_B). Substitute the values into the formula for d_B: d_B = (75)/((57.4^)) d_B ≈ (75)/(1.562309) d_B ≈ 48.006 m Step 4: Calculate the distance between the ship and the boat (D). Subtract d_B from d_S: D = d_S - d_B D = 151.299 m - 48.006 m D = 103.293 m Step 5: Round the answer to three significant figures. The distance between the ship and the boat, corrected to three significant figures, is: 103 m Drop the next question!