# Related Rates

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 2 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 5 ft from the wall? Evaluate your answer numerically. (Round the answer to three decimal places.)

1. 👍 0
2. 👎 0
3. 👁 197
1. let x be the horizontal distance from wall to ladder.

cosineTheta=x/10

10 cosTheta=x

-10sinTheta dTheta/dt= dx/dt

so you are looking for dTheta/dt

when x=5, theta = arccos.5, or 60 deg, and sin of 50 = .877

dTheta/dt= dx/dt / (10*.877)

check all that.

1. 👍 0
2. 👎 0
2. .228

1. 👍 0
2. 👎 0
posted by Jen

## Similar Questions

1. ### calculus

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

asked by Sasha on October 7, 2010
2. ### math

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

asked by Sasha on October 7, 2010
3. ### Calculus 1

Related Rates: 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 0.9 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the

asked by TayB on October 8, 2015
4. ### Calculus 1

A ladder 10ft long rests against a vertical wall. If the bottom on the ladder slides away from the wall at 2 ft/s, how fast is the angle ladder makes with the ground changing when the bottom of the ladder is 5 ft from the wall.

asked by Tina P on December 7, 2010
5. ### Calculus

A ladder 13 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1 ft. per second,how fast is the angle between the ladder and the ground changing when the bottom of the ladder

asked by Anonymous on April 13, 2016
6. ### Math

a ladder 10 ft long rests against a vertical wal. if the bottom of the ladder slides away from the wall at a rate of 0.7 ft/s, how fast is the angle between the ladder and the ground changing�

asked by Allie on March 29, 2010
7. ### Math 2

The bottom of the ladder rests on a horizontal flat surface and the top of the ladder rests against a wall. The ladder makes an angle of elevation of 61°. The bottom of the ladder is 6 ft from the base of the wall. How long is

asked by Tomiya on March 13, 2015
8. ### Calculus

A ladder 10 ft long rests against a vertical wall. If the bottom on the ladder slides away from the wall at 2 ft/s, how fast is the angle ladder makes with the ground changing when the bottom of the ladder is 5 ft from the wall?

asked by Tina P on December 7, 2010
9. ### Math

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 1.2 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft

asked by Aiton on December 12, 2008
10. ### Calc

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 1.3 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft

asked by Ash on September 30, 2018

More Similar Questions