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
Step 1: Draw a diagram to represent the situation. Let the height of the pole be h. Let the foot of the pole be point B and the top of the pole be point A. Let point M be on the horizontal ground, 10 m from the foot of the pole. This forms a right-angled triangle ABM, where the angle at B is 90^. The angle of elevation from M to the top of the pole (A) is AMB = 55^. The side AB is opposite to the angle 55^. The side BM is adjacent to the angle 55^. Step 2: Choose the appropriate trigonometric ratio. We know the adjacent side (BM = 10 m) and we want to find the opposite side (AB = h). The tangent function relates the opposite and adjacent sides: () = OppositeAdjacent Step 3: Set up the equation and solve for h. Substitute the given values into the formula: (55^) = (h)/(10) Multiply both sides by 10 to solve for h: h = 10 × (55^) Using a calculator for (55^): h ≈ 10 × 1.428148 h ≈ 14.28148 m Step 4: Round the answer to the nearest metre. h ≈ 14 m Comparing this to the given options: A. 7.0 m B. 8.0 m C. 6.0 m D. 14.0 m The correct option is D. The height of the pole is 14.0 m. Drop the next question.