A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At which rate is the angle between the string and the horizontal decreasing when 200 ft of string has been let out?

Q: A street light is at the top of a 18 ft tall pole. A woman 6 ft tall walks away from the pole with a…

A: Let x be the distance from the woman to the pole and y be the distance from the tip of the woman's…

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 ladder 13 ft long leans against a vertical wall. If the top slides down at 3 ft/s, how fast is the…

A: Follow the procedure given below.

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

A:

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

A:

Q: 1. A 15-meter ladder is resting against a vertical wall. If the bottom of the ladder is being pushed…

A: given: A 15-meter ladder is resting against a vertical wall. the bottom of the ladder is being…

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

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 street light is at the top of a 15 ft tall pole. A woman 6 ft tall walks toward the pole with a…

A:

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 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: A small rocket is launched straight up in the air at a speed of 4ft/sec. A camera on the ground, 10…

A: Consider the given information. At any time t, rocket is at C tanθ=ACAB=AC10

Q: A street light is at the top of a 16 ft tall pole. A woman 6 ft tall walks away from the pole with a…

A: Equation relates the number of variables combined together by algebraic entities using equality…

Q: An 8 ft ladder rests against a vertical wall. If the bottom of the ladder slides away from the wall…

A:

Q: A street light is at the top of a 17 ft tall pole. A woman 6 ft tall walks away from the pole with a…

A:

Q: A street light is at the top of a 14 ft tall pole. A woman 6 ft tall walks away from the pole with a…

A:

Q: A street light is at the top of a 16 ft tall pole. A woman 6 ft tall walks away from the pole with a…

A:

Q: A bird 150 ft above the ground flies horizontally at a speed of 11 ft/s. At what rate is the angle…

A: Given Data: The height of the bird above the ground is: y=150 ft The speed of the bird is: x'=11…

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: A street light is at the top of a 18 ft tall pole. A woman 6 ft tall walks away from the pole with a…

A: According to the given condition we haveIn this diagram, we have BC is the distance from the women…

Q: A woman standing on a cliff is watching a motor boat through a telescope as the boat approaches the…

A:

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: Please refer the attached image for complete solution. THANK YOU !

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

A:

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

A:

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: When a rocket is 3 kilometers high, it is moving vertically upward at a speed of 400 kilometers per…

A: Let the height of the rocket be h and the angle of elevation from the observer’s eye is x.

Q: An 8 ft. ladder rests against a vertical wall. If the bottom of the ladder slides away from the wall…

A:

Q: A street light is at the top of a 10 ft tall pole. A woman 6 ft tall walks away from the pole with a…

A:

Q: A street light is at the top of a 20 ft tall pole. A woman 6 ft tall walks away from the pole with a…

A: First draw the figure according to question is given and use similar traingle to find the rate of…

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

A: Diagram of the given question will be as following x is the distance of the man from pole y is the…

Q: When a rocket is 3 kilometers high, it is moving vertically upward at a speed of 400 kilometers per…

A:

Q: A man walks along a straight path at a speed of 6 ft/s. A searchlight is located on the ground 5 ft…

A: In the question it is asked to calculate at what rate the searchlight is rotating.

Q: An aircraft is climbing at a 300 angle to the horizontal. How fast is the aircraft gaining altitude…

A: An aircraft is climbing at a constant 30 degree angle to the horizontal and the speed is 500 mph…

Q: A ladder 15 ft. long leans against a vertical wall. If the top slides down at 2 ft/sec, how fast is…

A:

Q: A street light is at the top of a 16 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 4 ft/s. At what rate is the angle…

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

Q: A kite 100ft  above the ground moves horizontally at a speed of 8ft/s  At what rate is the angle…

A: Let x= horizontal distance L= length of string,  Then a rough sketch of the problem is as follows:

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 kite 100ft above the ground moves horizontally at a speed of 8 ft/s. At what rate is the angle…

A: Using triangle find angle then find the rate of change of angle

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. How fast is the top of the ladder sliding down the wall when the base of the ladder is 12 feet…

A: It is given that the length of ladder is 13 foot which acts as the hypotenuse of the right angled…

Q: A man walks along a straight path at a speed of 4ft/s. A searchlight is located on the ground 30…

A: Given data is : dxdt=4 ft/sec To find the Rate of the searchlight is rotating

Q: . A vertical cylinder is leaking water at a rate of 1 ft /sec. If the cylinder has a height of 10 ft…

A:

Q: An observer who is 3km from a launchpad watches a rocket that is rising vertically. At a certain…

A: Rate of change

Q: A hot air balloon is tethered at an angle of elevation of a/6. The rope holding the balloon is being…

A: Given Data: The angle of elevation is: α=π6 The rate at which the rope is being brought is: dxdt=-4…

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 ladder 9 ft long rests agains a vertical wall. If the bottom of the ladder slides away from the…

A: Let the distance between base B of the wall and bottom of the ladder C, BC= x feet  And the angle…

Q: g.) A ladder 14 ft long is leaning against a fence 8 ft high with the upper end projecting over the…

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.