5. A 200 foot tree is falling in the forest; the sun is directly overhead. At the moment when the tree makes an angle of 30° with the horizontal, its shadow is lengthening at the rate of 50 feet/sec. How fast is the angle changing at that moment?

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

A: Given, A ladder 10 ft long rests against a vertical wall. Let x be the distance between the bottom…

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: 8.A kite at an altitude of 200 ft. moves horizontally at the rate of 20 ft/sec. At what rate is the…

A: We have to find the rate of change of angle.

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

A:

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 6 ƒt tall Batman runs (into the night) away from a 10 ft streetlamp at a rate of 1 How fast is his…

A: The diagram of the situation is shown below:

Q: The base x of the right triangle in Figure increases at a rate of 5 emfs, while the height remains…

A: Write the tangent ratio for angle .

Q: A 25-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A:

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

A: Let the horizontal distance be x. From the given data of question: And the diagram is:

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

A: Given that

Q: A man 6 feet tall walks at a rate of 4 feet per second away from a light that is 15 feet above the…

A: Please see the explanation below

Q: A 6 ft tall Batman runs (into the night) away from a 10 ft streetlamp at a rate of 1 How fast is his…

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 15-meter ladder is resting against a vertical wall. if the bottom of the ladder is being pushed…

A:

Q: A ladder 10ft. long is resting against the side of a building if the foot of the ladder slips away…

A: Solved below

Q: 4.A ladder 10ft. long is resting against the side of a building if the foot of the ladder slips away…

A: This question is based on application of Derivative.

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

A:

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

A: Here we will find how fast is the balloon rising,

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

A:

Q: A 15-meter ladder is resting against a vertical wall, If the bottom of the ladder is being pushed…

A: Let ladder AB, l=15 m, Ladder is pushed horizontally at the rate of 1.5 m/s, ⇒dydt=1.5 We need to…

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

A:

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

A:

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

A:

Q: 12. A 7 ft tall person is walking away from a 20 ft tall lamppost at a rate of 5 f/sec. Assume the…

A:

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

A: Rate of change

Q: A ladder 14 ft long rests against a vertical wall. Let 0 be the angle between the top of the ladder…

A: Given:

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

A: Given : Length of the ladder = 20 ft

Q: Suppose you always keep your eyes fixed on the very top of a 100 m building. Suppose you start to…

A: Height of building = 100 m Let x be the base distance from the building Head angle = θ tanθ=100x

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 kite, 120 ft above the ground, is moving horizontally at the rate of 10 ft/sec. At what rate is…

A:

Q: s. How fast (in knots) is the distance between the ships changing at 4 PM? (Note

A:

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

A: To determine the rate of change of angle between the ladder and the ground.

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: A kite 100 ft above the ground moves horizontally at a speed of 4 ft/s. At what rate is the angle…

A: Here we use trigonometric formulas along with differentiation formulas.

Q: A kite 100 ft above the ground moves horizontally at a speed of 3 ft/s. At what rate is the angle…

A: The diagrammatic representation of the problem is shown below.

Q: A hot air balloon rising vertically is tracked by an observer located 7 km from the lift-off point.…

A:

Q: A hot air balloon rising vertically is tracked by an observer located 7 km from the lift-off point.…

A: Rate of change

Q: You are videotaping a race from a stand 132 ft from the track, following a car that is moving at 180…

A: To  Determine: How fast will your camera angle u be changing when the car is right in front of you?…

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 man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above the…

A:

Q: a television camera is positioned o the ground 4000 feet from the base of a rocket launching pad. If…

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.