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: Given A = (12)/(13), use the identity ^2 A + ^2 A = 1. ^2 A + ^2 A = 1 Step 2: Substitute A = (12)/(13). ^2 A = 1 - ( (12)/(13) )^2 Step 3: Compute ( (12)/(13) )^2. ( (12)/(13) )^2 = (144)/(169) Step 4: Simplify. ^2 A = 1 - (144)/(169) = (169)/(169) - (144)/(169) = (25)/(169) Step 5: Solve for A. A = ± sqrt((25)/(169)) = ± (5)/(13) Assuming acute angle, A = (5)/(13). (5)/(13) Step 1: Given B = (3)/(5), use the identity ^2 B + ^2 B = 1. ^2 B + ^2 B = 1 Step 2: Substitute B = (3)/(5). ^2 B = 1 - ( (3)/(5) )^2 Step 3: Compute ( (3)/(5) )^2. ( (3)/(5) )^2 = (9)/(25) Step 4: Simplify. ^2 B = 1 - (9)/(25) = (25)/(25) - (9)/(25) = (16)/(25) Step 5: Solve for B. B = ± sqrt((16)/(25)) = ± (4)/(5) Assuming acute angle, B = (4)/(5). (4)/(5)