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
For the first triangle, only two angles are given (20^ and 40^). To determine the absolute value of any side length (variables a, b, c), at least one side length must be provided. Since no side length is given, the unknown variables a, b, c cannot be determined numerically. For the second triangle: Given: A = 33^, C = 65^, side a = BC = 22. Unknown variables: side b = AC and side c = AB. Step 1: Calculate the third angle, B. The sum of angles in a triangle is 180^. B = 180^ - ( A + C) B = 180^ - (33^ + 65^) B = 180^ - 98^ B = 82^ Step 2: Use the Sine Rule to find side b. The Sine Rule states (a)/( A) = (b)/( B) = (c)/( C). Using (b)/( B) = (a)/( A): b = (a × B)/( A) Substitute the known values: b = (22 × 82^)/( 33^) b ≈ (22 × 0.990268)/(0.544639) b ≈ (21.7859)/(0.544639) b ≈ 39.9999 Rounding to 1 decimal place: b ≈ 40.0 Step 3: Use the Sine Rule to find side c. Using (c)/( C) = (a)/( A): c = (a × C)/( A) Substitute the known values: c = (22 × 65^)/( 33^) c ≈ (22 × 0.906308)/(0.544639) c ≈ (19.9388)/(0.544639) c ≈ 36.610 Rounding to 1 decimal place: c ≈ 36.6 The unknown variables in the second triangle are: b = 40.0 c = 36.6 Send me the next one 📸