A kite 50ft above the ground moves horizontally at a speed of 6ft/s. At what rate is the angle between the string and the horizontal decreasing when 300ft of string has been let out? Answer (in radians per second):

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: Let θ denote the angle between thw ladder and the ground

Q: A hot air ballon rises vertically upwards from a distance of 170m away. If the angle 0 at which you…

A: To Determine: how fast is the ballon rising when θ=π6 Given: A hot air balloon rises vertically…

Q: A hot air balloon rising vertically is tracked by an observer located 8 km from the lift-off point.…

A:

Q: A 10-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A: Length of ladder is l= 10ft X=8 ft, dx/dt= 18ft/sec From the fig l =[ x2 + y2 ]0.5= 10 a) from…

Q: A kite 100 ft above the ground moves horizontally at a speed of 10 ft/s. At what rate is the angle…

A:

Q: A street light is at the top of a 15 ft tall pole. A woman 6 ft tall walks away from the pole with a…

A:

Q: A 10-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A: Given that, the length of the ladder is 10 ft and distance between the wall and ladder in base is 6…

Q: A 10-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A:

Q: A hot air balloon rising vertically is tracked by an observer located 6 km from the lift-off point.…

A: Given y be the height of the Ballon ,t be time and theta the angle between the line of sight and the…

Q: A 13-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A: .

Q: A kite 100 ft above the ground moves horizontally at a speed of 5 ft/s. At what rate is the angle…

A: Let's solve given rate of change problem.

Q: A spy uses a telescope to track a rocket launched vertically from a launching pad 6 km away, as in…

A:

Q: You are stationary on the ground and are watching a bird fly horizontally towards you at a rate of 5…

A:

Q: A kite 100 ft above the ground moves horizontally at a speed of 13 ft/s. At what rate is the angle…

A:

Q: A hot air balloon rising vertically is tracked by an observer located 6 km from the lift-off point.…

A: The objective of the problem is to find the speed at which the balloon is rising at the given…

Q: A 10-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A:

Q: A hot air balloon rising vertically is tracked by an observer located 3 km from the lift-off point.…

A: topic - trigonometric ratios and application of derivatives

Q: A spy uses a telescope to track a rocket launched vertically from a launching pad 6 km away, as in…

A: Given that

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A:

Q: A man 6 ft tall is walking at the rate of 3 ft/s toward a streetlight 18 ft high (see Figure 1). (a)…

A: By using similarity rule:

Q: A 10-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A:

Q: A jet airliner is flying at a constant altitude of 12,000 ft above sea level as it approaches a…

A: The diagram of a jet airliner A traveling at a constant height toward a radar station R is shown…

Q: An airplane is flying in still air with an airspeed of 284 miles per hour. If it is climbing at an…

A: We have to apply the application of trigonometry

Q: If a ladder of length 20 ft which is leaning against a vertical wall has its upper end sliding down…

A: Given:         Length of ladder =20 ft    dhdt=-2 ft/sec

Q: An airplane is flying horizontally at an altitude of 9000 m. An observer on the ground noticed that…

A:

Q: Need help solving this and worked out solution im confused as to where to start. Its related rates

A: It is given that the kite 100 ft above the ground moves horizontally at a speed of 14 ft/s.

Q: A hot air balloon rising vertically is tracked by an observer located 3 km from the lift-off point.…

A: topic- application of derivatives

Q: (c) Find the rate at which the angle between the ladder and thewall of the house is changing when…

A: Let θ = angle between top of ladder and wall   Let x = distance from base of ladder to wall   Base…

Q: 10-ft ladder is leaning against a house when its base starts to slide away. By the time the base is…

A:

Q: A hot air balloon rising vertically is tracked by an observer located 6 km from the lift-off point.…

A:

Q: A street light is at the top of a 13 ft tall pole. A woman 6 ft tall walks away from the pole with a…

A:

Q: A kite 100 ft above the ground moves horizontally at a speed of 12 ft/s. At what rate is the angle…

A: Height of kite flying above the ground is 100 ft Horizontal speed of kite is 12 ft/s We have to find…

Q: A kite 100 ft above the ground moves horizontally at a speed of 10 ft/s. At what rate is the angle…

A:

Q: A man walks along a straight path at a speed of 5 ft/s. A search light is located on the ground 12…

A: Hypotenuse is the longest side of any right angle triangle. Pythagoras theorem states that the…

Q: A kite 100 ft above the ground moves horizontally at a speed of 11 ft/s. At what rate is the angle…

A: For the given scenario, a rough sketch is as follows:

Q: A hot air balloon rising vertically is tracked by an observer located 4 km from the lift-off point.…

A: A Hot air balloon is rising vertically . Angle between observer's line of sight and ballon is pi/5.…

Q: A winch is on top of a pole that is 25 ft high and it is using a rope to pull object A. The rope is…

A: Let the distance of the object from the wall is x. the length of the rope is L and the length of the…

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: Given that: Distance from the bottom of the wall, x=8 ftLength of ladder, L=10 ftSliding speed of…

Q: A 10​-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A: Given: A 10​-ft ladder is leaning against a house when its base starts to slide away. By the…

Q: The figure below shows a camera mounted at a point 6000 ft from the base of a rocket launching pad.…

A:

Q: A 13-foot long ladder is leaning against the side of a house when its base starts to slide away. By…

A:

Q: A street light mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole…

A: Given information:   Height of the pole AC= 15ft and DE = 6ft is the height of the man and length of…

Q: A 15 feet long ladder is leaning against the wall. The bottom of the ladder is sliding away from the…

A:

Q: A man 6 ft tall is walking at the rate of 3 ft/s toward a streetlight 18 ft high (see Figure 1). (a)…

A:

Q: 9. A balloon, leaving the ground 60 ft. from the observer, rises 10 ft. per sec. How fast is the…

A: 9- Given- The ballon leaving the ground 60ft. from the observer rises 10 feet per second. To find-…

Q: 10. A ladder 13 ft. long leans against a vertical wall. If the top slides down at 1.5 ft. per sec.,…

A: Definition used-         In a right angle triangle -…

Q: A hot air balloon rising vertically is tracked by an observer located 8 km from the lift-off point.…

A: From the given information we use trig ratio ,  tan(θ)=oppositeadjacent…

Q: A 13-ft ladder is leaning against a house when its base starts to slide away (see accompanying…

A: Let the distance of the base from the wall is x ftAnd the top of the ladder is y ft high. Then x and…

Q: 1. A 13-ft ladder is leaning against a house when its base is being pushed towards the wall. By the…

A:

Q: A street light is at the top of a 19 ft tall pole. A woman 6 ft tall walks away from the pole with a…

A:

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.