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
m, let's knock this out. Step 1: Determine A and A from A = (1)/(2). Since A is an acute angle, we can form a right-angled triangle where the opposite side is 1 and the adjacent side is 2. The hypotenuse h_A is calculated using the Pythagorean theorem: h_A = sqrt(1^2 + 2^2) = sqrt(1 + 4) = sqrt(5) Therefore, A = oppositehypotenuse = (1)/(sqrt(5)) A = adjacenthypotenuse = (2)/(sqrt(5)) Step 2: Determine B from B = (3)/(5). Since B is an acute angle, we can form a right-angled triangle where the adjacent side is 3 and the hypotenuse is 5. The opposite side o_B is calculated using the Pythagorean theorem: o_B = sqrt(5^2 - 3^2) = sqrt(25 - 9) = sqrt(16) = 4 Therefore, B = oppositehypotenuse = (4)/(5) Step 3: Use the sum formula for sine, (A+B) = A B + A B. Substitute the values found in Step 1 and Step 2: (A+B) = ((1)/(sqrt(5))) ((3)/(5)) + ((2)/(sqrt(5))) ((4)/(5)) (A+B) = (3)/(5sqrt(5)) + (8)/(5sqrt(5)) (A+B) = (3+8)/(5sqrt(5)) (A+B) = (11)/(5sqrt(5)) This matches option (a). The final answer is (a) (11)/(5sqrt(5)). Send me the next one 📸