# Related Rates

posted by .

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.)

• Related Rates -

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.

• Related Rates -

.228

## Similar Questions

1. ### 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 …
2. ### 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 when the bottom of the ladder is 6 ft fro the wall?

A ladder 20 ft long rests against a vertical wall. Let \theta 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 …
4. ### calculus

A ladder 14 ft long rests against a vertical wall. Let \theta 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 …
5. ### 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 …
6. ### 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 …
7. ### 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.
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?
9. ### 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 …
10. ### 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 is …

More Similar Questions