A balloon released at point P rises vertically with a constant speed of 6 m/s. Point Q is level with and 75 m distant from point P. How fast is the angle of elevation of the balloon at Q changing when the balloon is 100 m above P?

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 20-foot-tall tree has fallen against the wall of a garage. The base of the tree starts to slide on…

A:

Q: The bast x of the right triangie in the figure, increases at a rate of 5 cm/s, while the nei ght…

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:

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: When a rocket is 5 kilometers high, it is moving vertically upward at a speed of 900 kilometers per…

A:

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

A:

Q: A kite 160 feet above the ground moves in a direction parallel to the ground at the rate of 5 feet…

A: Let, x= the horizontal distance of the kite y=the length of the string Given that dx/dt=5 ft/sec  We…

Q: A    26    foot    ladder    is    sliding    down    a    vertical    wall.        The    base…

A:

Q: A ladder that is 3 meters long is leaning against a wall. The base of the ladder slides away from…

A:

Q: A 10 foot ladder is leaning against a wall, with its base 3 feet from the wall. It begins to slide…

A: Given that A 10 foot ladder is leaning against a wall, with its base 3 feet from the wall. It begins…

Q: A man walks along a straight path at a speed of 4 ft/s. A searchlight is located on the ground 20 ft…

A:

Q: A plane flies at a speed 540 km/hr at a constant height of 10 km. How rapidly is the angle of…

A:

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

A:

Q: A weather balloon is rising vertically at the rate of 5 meters per second. An observer is standing…

A:

Q: A ladder 25 ft long is leaning against a wall. If the bottom of the ladder is pulled 10.…

A: We need to find change in angle.

Q: A rock is tossed at an initial velocity of 60 m/s at an angle of 10° with the ground. After 0.9…

A: The solution of above question is written below.

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

A: Given thatLadder length = 10 ftDistance of ladder from the bottom of wall = 6 ftRate of change of…

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

A:

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

A:

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

A: Given that a ladder 10 ft. long leans against a vertical wall. Bottom of the ladder slides away from…

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

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

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: When a rocket is 6 kilometers high, it is moving vertically upward at a speed of 600 kilometers per…

A: Set the height of the rocket be h and angle of elevation from the observer's eye is x. dhdt=600

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 13-ft ladder is leaning against a house when itsbase starts to slide away. By the time thebase is…

A: Given: length of ladder, L=13 ft distance from base, x = 12 ft dxdt=5 ft/sec

Q: When a rocket is 10 kilometers high, it is moving vertically upward at a speed of 1000 kilometers…

A: To determine the rate of change of angle of elevation with respect to observer.

Q: 2.) A ladder 5 feet long rests against a vertical wall. If the bottom of the ladder (on level…

A: A ladder is 5 feet long. The speed at which the ladder slides away from the wall is 1 foot per…

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

A:

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

A: l = length of ladder y = height of ladder from the ground x = distance moved away from the wall…

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

A:

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 triangle has two constant sides of length 6 ft and 2 ft. The angle between these two sides is…

A:

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: An airplane is flying on a horizontal path at the height of 3,800 feet. At what rate is the distance…

A: We need to find rate of distance changing.   ddθ(cscθ)=-csc(θ)cot(θ)

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

A:

Q: A ladder 10 ft long leans against a vertical wall. If the bottomof the ladder slides away from the…

A: Given - A ladder 10 ft. long leans against a vertical wall. If the bottom of the ladder slides away…

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

A:

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 kite is flying 25 meters above the flat Earth and being blown by the wind in the horizontal…

A: To calculate rate of change of angle between kite and grounds.  Let theta is the angle between kite…

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.