There is a right triangle with x and y legs labeled B and A, respectively. B is increasing at a rate of 1 m/s and A is decreasing at a rate of 2 m/s. At what rate is the angle theta (located on the leg B) changing when A is 10m and B is 20m?
tan theta=A/B
B tan Theta=A
tanTheta dB/dt+ B*dtan/dt=dA/dt
tanTheta dB/dt + B sec^2 theta dTheta/dt=dA/dt
put in A, B, dB/dt, dA/dt, for tan theta=2, sec^2 theta= A^2/(a^2+b^2)
solve for dTheta/dt