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: Find the third angle of the triangle. The sum of angles in a triangle is 180^. BAC = 180^ - ABC - ACB BAC = 180^ - 59^ - 73^ BAC = 180^ - 132^ BAC = 48^ Step 2: Use the Sine Rule to find the length of side AC. The Sine Rule states (a)/( A) = (b)/( B) = (c)/( C). We have |BC| = 12 cm, BAC = 48^, ABC = 59^, and ACB = 73^. To find |AC|, we use the ratio: (|AC|)/(( ABC)) = (|BC|)/(( BAC)) |AC| = (|BC| × ( ABC))/(( BAC)) |AC| = (12 × 59^)/( 48^) |AC| = (12 × 0.857167)/(0.743145) |AC| ≈ 13.84 cm Step 3: Use the Sine Rule to find the length of side AB. To find |AB|, we use the ratio: (|AB|)/(( ACB)) = (|BC|)/(( BAC)) |AB| = (|BC| × ( ACB))/(( BAC)) |AB| = (12 × 73^)/( 48^) |AB| = (12 × 0.956305)/(0.743145) |AB| ≈ 15.44 cm The lengths of the remaining two sides are: |AC| ≈ 13.84 cm |AB| ≈ 15.44 cm Send me the next one 📸