Please help! Will give brainliest, also 20 points, correct answers only!!

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Ответ:

judyewert

20.09.2021

Mathematics

$9\ ft/rad$

Step-by-step explanation:

Given

Length of the ladder is $l=18\ ft$

Angle between the wall and the ladder is $\theta$

from the figure, we can write

$\Rightarrow \sin \theta=\dfrac{x}{18}\\\\\Rightarrow x=18\sin \theta$

Differentiate the above equation w.r.t $\theta$

$\Rightarrow \dfrac{dx}{d\theta}=18\cos \theta\\\\\text{at }\theta=\dfrac{\pi }{3}\\\\\Rightarrow \dfrac{dx}{d\theta}=18\cos(\dfrac{\pi}{3})\\\\\Rightarrow \dfrac{dx}{d\theta}=18\times 0.5\\\\\Rightarrow \dfrac{dx}{d\theta}=9\ ft/rad$

A ladder 18 ft long rests against a vertical wall. Let θ be the angle between the top of the ladder

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