Question

A ladder 54 feet tall is place against a tall building. The bottom of the ladder is sliding away from the building horizontally at a rate of 5 feet/sec. Find the rate at which the indicated angle, θ , is changing when the angle is 26 degrees . Express your answer in radians per sec and round to four decimals.

Answer 1

If the foot of the ladder is x feet from the wall, we have
cosθ = x/54
-sinθ dθ/dt = 1/54 dx/dt
when θ=26°, you have
dθ/dt = -5/(54 sin26°) = -.21 = -12°/s

Answer 2

thank you so much i understand it now!