The angle between the ladder and the ground is - 0.075 rad/s.
Pythagoras' theorem is a essential relation in Euclidean geometry among the 3 facets of a proper triangle. It states that the region of the rectangular whose aspect is the hypotenuse (the aspect contrary the proper angle) is identical to the sum of the regions of the squares on the alternative facets.
cosθ = x/10
On differentiating the above equation,
- sinθdθ/dt = (1/10)dx/dt
dθ/dt = -(1/10)dx/dt/sinθ
sinθ = y/10
= √(100 - 36)/10
= 0.8; dθ/dt
= -(1/10)·0.6 ft/s/0.8
= - 0.075 rad/s
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