If sin A = 3/5 and cos B = 4/5, where A and B are acute

Solution

We are given sin A = 3/5. Using the Pythagorean identity: cos A = √(1 - sin²A) = √(1 - (3/5)²)  = √(1 - 9/25) = √(16/25)  = 4/5. Similarly, we are given cos B = 4/5. Using the Pythagorean identity: sin B = √(1 - cos²B) = √(1 - (4/5)²)  = √(1 - 16/25) = √(9/25)  = 3/5. Using the formula for sin(A + B): sin(A + B) = sin A cos B + cos A sin B. sin(A + B) = (3/5)(4/5) + (4/5)(3/5)  = 12/25 + 12/25 = 24/25  = 0.96. Correct answer: a) 0.96