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: Define the variables and set up the trigonometric relationships. Let D be the horizontal distance from the observation point to the building, D = 20 m. Let h_1 be the height from the ground to the bottom of the window. Let h_2 be the height from the ground to the top of the window. The angle of elevation to the bottom of the window is _1 = 27^. The angle of elevation to the top of the window is _2 = 32^. The height of the window, H, is h_2 - h_1. We use the tangent function, which relates the opposite side (height) to the adjacent side (distance): () = oppositeadjacent Step 2: Calculate the height to the bottom of the window (h_1). (_1) = (h_1)/(D) (27^) = (h_1)/(20) h_1 = 20 × (27^) Using a calculator, (27^) ≈ 0.509525. h_1 = 20 × 0.509525 h_1 ≈ 10.1905 m Step 3: Calculate the height to the top of the window (h_2). (_2) = (h_2)/(D) (32^) = (h_2)/(20) h_2 = 20 × (32^) Using a calculator, (32^) ≈ 0.624869. h_2 = 20 × 0.624869 h_2 ≈ 12.4974 m Step 4: Calculate the height of the window (H). The height of the window is the difference between h_2 and h_1. H = h_2 - h_1 H = 12.4974 m - 10.1905 m H = 2.3069 m Rounding to two decimal places: H ≈ 2.31 m The height of the window is 2.31 m. That's 2 down. 3 left today — send the next one.