A ladder 10 ft long rests against a vertical wall. let θ be the angle between the top of the ladder and the wall and let x be the distance from the bottom of the ladder to the wall. If the bottom of the ladder slides away from the wall, how fast does x change with respect to θ when θ = π/3

Answer 1

According to you diagram I have

cos Ø = x/10
x = 10cosØ
dx/dØ = -10sinØ

so when Ø=π/3
dx/dØ = -10sin π/3
= -10 (√3/2)

Answer 2

SinØ = opp/hyp
opp is x
hyp is 10

SinØ = x/10
10SinØ = x

Sin (π/3) = 1/2
10 * 1/2 = 5

Answer: 5 ft/rad