Ladder problem Rate of change of height?

Question

A ladder is placed 50 meters from a wall at and angle θwith the horizontal the top of the laader

iis xmeters above the ground. If the bottom of the ladder is pushed toward the wall, find the rate of change

of x with respect to θ when θ = 45o

Answer 1

x/50 = tan(θ)

x = 50tan(θ)

dx/dθ = 50 sec²(θ)

When θ = 45°, sec²(45) = (√2)² = 2

dx/dθ = 50(2) = 100