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
To find the height of the storey building, we can use trigonometry. Step 1: Determine the height difference from the top of the building to the mango. Let x be the vertical distance from the top of the building to the level of the mango. The horizontal distance from the base of the building to the tree is 20 m. The angle of depression from the top of the building to the mango is 68^. In the right-angled triangle formed, the opposite side to the angle of depression is x, and the adjacent side is 20 m. We use the tangent function: () = oppositeadjacent (68^) = (x)/(20 m) x = 20 m × (68^) x ≈ 20 m × 2.4751 x ≈ 49.502 m Step 2: Calculate the total height of the building. The total height of the building (H) is the sum of the vertical distance x and the height of the mango above the ground (4.5 m). H = x + 4.5 m H ≈ 49.502 m + 4.5 m H ≈ 54.002 m Step 3: Round the height to the nearest metre. H ≈ 54 m Comparing this to the given options, the closest option is (B). The final answer is B) 54 m. That's 2 down. 3 left today — send the next one.