Final answer:
To find A and B, we solve the equations tan(A-3) = 0 and tan(A+B) - 5, given A+B = 90. By solving these equations, we find that A = 3 and B = 87.
Step-by-step explanation:
We have two equations to work with: tan(A+B) - 5 and tan(A-3) = 0. We also know that A+B = 90. Let's start by solving the second equation: tan(A-3) = 0. Since tangent equals zero when the angle is zero, we can set A-3 = 0, which gives us A = 3.
Now that we know A is 3, we can substitute this value into the first equation: tan(3+B) - 5 = 0. Rearranging the equation, we get tan(3+B) = 5. Since 3+B = 90 (because A+B = 90), we can calculate B by subtracting 3 from 90, giving us B = 87.
Therefore, A = 3 and B = 87.