(Solved): A ladder 10ft long rests against a vertical wall. If the bottom of the ladder slides away from the ...

A ladder $10\mathrm{ft}$ long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of $0.9\mathrm{ft}/\mathrm{s}$, how fast (in rad/s) is the angle (in radians) between the ladder and the ground changing when the bottom of the ladder is $8\mathrm{ft}$ from the wall? (That is, find the angle's rate of change when the bottom of the ladder is $8\mathrm{ft}$ from the wall.) $\times \mathrm{rad}/\mathrm{s}$ Enhanced Feedback Please try again. Let $?$ denote the angle between the ladder and the ground. You should use the appropriate trigonometric function to relate the angle $?$ with $x$ and then differentiate (with respect to $t$ ) the relation on both sides using the Chain Rule. You will also need to use the Pythagorean Theorem to find the value of $y$ that will allow you to find the trigonometric values needed. Note that negative rate means the quantity is decreasing.