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 in the right-angled triangle. We are given: • An angle = 40^. • The side adjacent to the 40^ angle is 8. • The side opposite to the 40^ angle is x. 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. (40^) = (x)/(8) Step 4: Solve for x. Multiply both sides by 8: x = 8 × (40^) Step 5: Calculate the value of x. Using a calculator for (40^): (40^) ≈ 0.8391 x = 8 × 0.8391 x ≈ 6.7128 Step 6: Round the answer to two decimal places. x ≈ 6.71 The value of x is: 6.71