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: Identify the known values and the unknown value. • The angle of elevation () is 36^. (Assuming "360" is a typo and should be 36^, as 360^ would imply the point is directly above the base, not 42 m away). • The distance from the base of the tower (adjacent side) is 42 m. • The height of the tower (opposite side) is h. Step 2: Choose the appropriate trigonometric ratio. The tangent function relates the opposite side, the adjacent side, and the angle: () = oppositeadjacent Step 3: Substitute the given values into the formula. (36^) = (h)/(42) Step 4: Solve for h. Multiply both sides by 42: h = 42 × (36^) Step 5: Calculate the value of h. Using a calculator for (36^): (36^) ≈ 0.7265 h = 42 × 0.7265 h ≈ 30.513 m Step 6: Round the answer to a reasonable number of decimal places (e.g., two decimal places). h ≈ 30.51 m The height of the tower is: 30.51 m