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
Okay, let's solve for x and h. Step 1: Write down the given equations and the values of the tangent functions. We are given two equations: 1) h = x 60^ 2) h = (x + 1000) 30^ We know that 60^ = sqrt(3) and 30^ = (1)/(sqrt(3)). Step 2: Substitute the tangent values into the equations. Substitute 60^ = sqrt(3) into equation (1): h = xsqrt(3) (3) Substitute 30^ = (1)/(sqrt(3)) into equation (2): h = (x + 1000)(1)/(sqrt(3)) (4) Step 3: Equate the expressions for h to solve for x. Set equation (3) equal to equation (4): xsqrt(3) = (x + 1000)(1)/(sqrt(3)) Multiply both sides by sqrt(3) to eliminate the fraction: xsqrt(3) · sqrt(3) = (x + 1000)(1)/(sqrt(3)) · sqrt(3) 3x = x + 1000 Subtract x from both sides: 3x - x = 1000 2x = 1000 Divide by 2: x = (1000)/(2) x = 500 metres Step 4: Substitute the value of x into equation (3) to find h. Using h = xsqrt(3) and x = 500: h = 500sqrt(3) To get a numerical value, use sqrt(3) ≈ 1.732: h = 500 × 1.732 h = 866 metres The values are: x = 500 metres h = 866 metres 3 done, 2 left today. You're making progress.