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
a) Step 1: Identify the given values and the unknown height. We have a right-angled triangle TRO. The distance from the observer to the tower base, |OR|, is 84 m. The angle of elevation from O to T is 57^. Let the height of the tower TR be h. Step 2: Use the tangent function to find the height h. In TRO, () = oppositeadjacent. (57^) = (TR)/(OR) (57^) = (h)/(84) h = 84 × (57^) h ≈ 84 × 1.53986496 h ≈ 129.3486566 Step 3: Round the height to three significant figures. h ≈ 129 m b) Step 4: Identify the new angle and the unknown new distance. The observer moves away, and the new angle of elevation is 49^. Let the new distance from the tower base to the observer be OR'. Using the height h calculated in part (a) (using the unrounded value for accuracy): (49^) = (h)/(OR') OR' = (h)/((49^)) OR' = (129.3486566)/((49^)) OR' ≈ (129.3486566)/(1.15036736 OR' ≈ 112.4400 m) Step 5: Calculate how far the observer moved backwards. The distance moved backwards is the difference between the new distance and the original distance. Distance moved = OR' - OR Distance moved ≈ 112.4400 - 84 Distance moved ≈ 28.4400 m Step 6: Round the distance moved to two decimal places. Distance moved ≈ 28.44 m Send me the next one 📸