A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.8 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 6 ft from the wall? (That is, find the angle's rate of change when the bottom of the ladder is 6 ft from the wall.)

Question
Asked Nov 8, 2019
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A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.8 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 6 ft from the wall? (That is, find the angle's rate of change when the bottom of the ladder is 6 ft from the wall.)

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Expert Answer

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Step 1

Given that

Ladder length = 10 ft

Distance of ladder from the bottom of wall = 6 ft

Rate of change of ladder of wall from the bottom of wall = 0.8 ft/s

Step 2

To determine angle change of ladder from the bottom of wall

Step 3

Calculation

Ladder and wall makes a right angle triangle where ladder as hypotenuse and distance fro...

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Image Transcriptionclose

base cose hypotenuse 6 cose 10 -53.130 cos 10

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Math

Calculus