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: Convert the angle from degrees and minutes to decimal degrees. Given m( C) = 54^ 13'. To convert minutes to degrees, divide by 60. 13' = (13)/(60)^ ≈ 0.2167^ So, m( C) ≈ 54.2167^. Step 2: Identify the trigonometric relationship. In a right-angled triangle ABC with the right angle at B: • The side opposite to C is AB. • The side adjacent to C is BC. The tangent function relates the opposite and adjacent sides: ( C) = oppositeadjacent = (AB)/(BC) Step 3: Substitute the given values into the equation. We are given m( C) = 54^ 13' and BC = 20 cm. (54^ 13') = (AB)/(20) Step 4: Solve for AB. Multiply both sides by 20: AB = 20 × (54^ 13') AB = 20 × (54.2167^) Using a calculator: AB ≈ 20 × 1.3868 AB ≈ 27.736 Rounding to one decimal place, the length of AB is approximately 27.7 cm. The length of AB is 27.7 cm. That's 2 down. 3 left today — send the next one.