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
Another one More — let's solve it. Step 1: Define variables and set up the diagram based on the problem description. Let h be the height of the building (from the ground level at S to the top of the building, B). Let x be the horizontal distance from point S (and T) to the base of the building. Let P be the base of the building, so BP = h. Point T is vertically above S, with ST = 30 m. Draw a horizontal line from T to the building, meeting it at point Q. Then PQ = ST = 30 m. The height from Q to the top of the building B is BQ = BP - PQ = h - 30. Step 2: Formulate equations using trigonometry for the angle of elevation from S. From point S, the angle of elevation to the top of the building B is 70^. In the right-angled triangle formed by B, P, and S: (70^) = oppositeadjacent = (BP)/(SP) = (h)/(x) This gives us our first equation: h = x (70^) (1) Step 3: Formulate equations using trigonometry for the angle of elevation from T. From point T, the angle of elevation to the top of the building B is 20^. In the right-angled triangle formed by B, Q, and T: (20^) = oppositeadjacent = (BQ)/(QT) = (h - 30)/(x) This gives us our second equation: h - 30 = x (20^) (2) Step 4: Solve the system of equations for h. From equation (1), we can express x in terms of h: x = (h)/((70^)) Substitute this expression for x into equation (2): h - 30 = ((h)/((70^))) (20^) h - 30 = h ((20^))/((70^)) Rearrange the equation to solve for h: h - h ((20^))/((70^)) = 30 Factor out h: h (1 - ((20^))/((70^))) = 30 To simplify the term in the parenthesis, find a common denominator: h (((70^) - (20^))/((70^))) = 30 Now, isolate h: h = (30 (70^))/((70^) - (20^)) Step 5: Calculate the numerical value of h. Using a calculator: (70^) ≈ 2.747477 (20^) ≈ 0.363970 Substitute these values into the equation for h: h = (30 × 2.747477)/(2.747477 - 0.363970) h = (82.42431)/(2.383507) h ≈ 34.5890 Rounding to two decimal places: h ≈ 34.59 m The height of the building is 34.59 m. Got more? Send 'em 📸