Calculus II
posted by Lynn .
A 24 foot ladder is leaning against a building. Let x be the distance between the bottom of the ladder abd the building and let theta be the angle between the ladder and the ground. Suppose the bottom of the ladder is sliding away from the wall at a rate of 2 ft/sec. When x=6, how fast is theta (in Radians/sec) changing?

cosØ = x/24
sinØ dØ/dt = (1/24)dx/dt
when x = 6, opposite side is y
y^2 + 6^2 = 24^2
y = √540 and sinØ = √540/24
dØ/dt = 1/(24sinØ)dx/dt
= (1/24)(24/√540)(2) = 2/√540 rad/sec
simplify as needed
Respond to this Question
Similar Questions

math word problems
A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 9 ft less than the length of the ladder.how high up the side of the building is the top of the ladder if that distance is 2 ft less … 
Calculus Ab
A 26 foot step ladder is leaned up against a 30 foot building to reach a window near the top. The ladder is being pushed toward the building in a horizontal direction of 2 feet per second. 1. Find each related rate when the ladder … 
Calculus
a 16 foot ladder is leaning against a building. the bottom of the ladder os sliding along the pavement at 3 ft/s How fast is the top of the ladder moving down when the foot of the ladder is 2 ft from the wall 
Calculus
A 24 foot ladder is leaning against a building. Let x be the distance between the bottom of the ladder and the building and let theta be the angle between the ladder and the ground. a)Express theta as a function of x. cos theta = x/24 … 
Math trig
a ladder 24 feet long leans against the side of a building, and the angle between the ladder and the building is 25°. a) approximate the distance from the bottom of the ladder to the building. b)if the distance from the bottom of … 
algebra 2
A ladder of 25ft is placed against a building in such a way that the distance from the top of the ladder to the ground is 12ft more than the distance from the bottom of the ladder to the building. What is the quadratic equation used … 
geometry
A 7foot ladder is leaned against a building in such a way that the bottom of the ladder is 4 feet from the base of the wall. Find the angle formed between the ladder and the ground. 
calculus
a ladder 6 feet long leans against a vertical building. the bottom of the ladder slides away from the building horizontally at rate of 1/2 ft/sec. A) at what rate is the top of the ladder sliding down the wall when the bottom of the … 
trigonometry
A 10 meter ladder is leaning against the side of a building. If the bottom of the ladder is 3 meters from the bottom of the building, find the measure of the acute angle that the ladder makes with the building. 
Calculus
a 12 foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 1 feet/second, how fast is the top of the ladder moving down when the foor of the ladder is …