Height of a Balloon A 680-ft rope anchors hot-air balloon as shown in the figure.           (a) Express the angle θ as a function of the height h of the balloon.           (b) Find the angle θ if the balloon is 500ft high.

Q: 65. Range of a Projectile If a projectile is fired with velocity vD at an angle 0, then its range,…

A:

Q: Angle of Depression A man is flying in a hot-air balloon in a straight line at aconstant rate of 5…

A: Given that, a man flying in a hot air balloons in a straight line with constant rate 5 feet per…

Q: 680 ft (a) Express the angle 0 as a function of the height h of the balloon. h 0 = sin 680 (b) Find…

A: Given : h = 600 Then, θ = sin-1(600/680) θ = sin-1(0.88234) θ = 61.9°

Q: Angle θ intersects the unit circle at point (-0.9483, -0.3173). What is the value of tan(θ)? a…

A: Coordinates of the unit circle for angle θ are given as ( cosθ , sinθ )  Hence,  cosθ  =  - 0.9483…

Q: The height (in meters) of a person on a Ferris wheel as a function of the angle from the 3 o'clock…

A:

Q: x is an acute angle. Find the value of x in degrees. cot (x) = 3 X =

A: Use trigonometric function

Q: The grade resistance F of a car traveling up or down a hill is modeled by the equation F = W sin θ,…

A: A car traveling up or down a hill is modeled by the equation F = WSinθ Find the weight of the card…

Q: f(x) = r2 cos(r) - 2r sin(r - 2 cos(r)

A:

Q: Problem: A bamboo pole is broken at a point 2.3 meters above the ground, and the end of the pole…

A:

Q: Range of a Projectile If a projectile is fired with velocity vo at an angle 0, then its range, the…

A:

Q: Trigonometric Functions On a particular lake, the difference between high and low tide is 6 hours.…

A: Given: The difference between high and low tide is 6 hours. From midnight till morning 6 am, its a…

Q: A shoreline observation post is located on a cliff such that the observer is 290 feet above sea…

A:

Q: of the rod to the water? 10 ft Figure for 41

A: Question   angle of elevation of  a fish is reeled in a rate1 foot per second from the point 10…

Q: Projectile motion A gun with muzzle velocity of 1200 ft/ sec is fired at an angle of 8° above the…

A:

Q: An observer views a rocket take off from a distance of 6 miles from the launch pad, and elevation.…

A: From the given information , we got a right angle triangle tan (θ)=opposite side adjacent sidetan…

Q: A boat approaches a 50-ft-high lighthouse whose base is at sea level. Let d be the distance between…

A: Given, Height of Light house- 50ft Distance between the boat and the base of the light house is 'd'…

Q: HOW DO YOU SEE IT? Write expressions for the tangent of each acute angle in the right triangle. A.…

A: The given triangle is right angle triangle. In right angle triangle ABC right angle at C., We know…

Q: 43. Height of a Balloon A 680-ft rope anchors a hot-air balloon as shown in the figure. (a) Express…

A: We have to find angle theta given in diagram.

Q: 6) Calculating the Time of a Trip From a parking lot, you want to walk to a house on the beach. The…

A: Given,  From a parking lot, you want to walk to a house on the beach.  The house is located 1500…

Q: HOW DO YOU SEE IT? Consider an angle in standard position with $r=12$ centimeters, as shown in the…

A: Given a figure with angle Given a figure with angle θ , length from (0,0) and (x,y) is 12 cm.

Q: From a vertical cliff on the bank of the Bueg river, the angle of depression of the opposite bank is…

A: This question is related to trignometry, we will solve it using given information.

Q: Trigonometric Functions of Quadrantal AnglesEvaluate the cosine and tangent functions at the…

A:

Q: Using the Unit Circle Use the unit circle to verifythat the cosine and secant functions are even and…

A: Using the Unit Circle Use the unit circle to verifythat the cosine and secant functions are even and…

Q: Angle φ intersects the unit circle at point (0.1495, 0.9888). What is the value of sin(φ)? A 0.1512…

A: To find the angle

Q: Height of a Rocket A rocket fired straight up is tracked by an observer onthe ground 1mi away.(a)…

A:

Q: Area of a Sector Find the area of the sector of a circle ofradius 3 centimeters formed by an angle…

A: The sector of a circle of radius 3 centimeters formed by an angle of 60°.

Q: 5. Projectile motion A gun with muzzle velocity of 1200 ft/sec is fired at an angle of 8° above the…

A:

Q: Ahmed boards a Ferris wheel at the 3-o'clock position and rides the Ferris wheel for several…

A: Here we solve the ferris wheel problem.

Q: Height of a Pole A 50-ft pole casts a shadow as shown in the figure. (a) Express the angle of…

A:

Q: Justin boards a Ferris wheel at the 3-o'clock position and rides the Ferris wheel for several…

A: Given- Justin boards a Ferris wheel at the 3-o'clock position and rides the Ferris wheel for several…

Q: Viewing angles An auditorium with a flat floor has a large flat-panel television on one wall. The…

A: We have given the actual problem : Where AC=10 ft,AB=7 ft,OC=10 ft,BC=3 ft We have to find the…

Q: A shoreline observation post is located on a cliff such that the observer is 290 feet above sea…

A:

Q: Observing a launch An observer stands 300 ft from the launchsite of a hot-air balloon. The balloon…

A: GivenObserver stands from the launch of a hot air ballon=300ft.Velocity…

Q: 4-2 2. Using reference angles, evaluate the functions. (a) | cos(240°) (b) tan(-135°) (c) sin(중m)

A:

Q: x is an acute angle. Find the value of x in degrees. tan (x) = 1 %3D X = Submit

A: Here we find acute angle x

Q: Collin boards a Ferris wheel at the 3-o'clock position and rides the Ferris wheel for several…

A: The rate of change of angle covered by a point per unit time is called the angular velocity of the…

Q: *5. A water wheel (used for power in the 18th century) is illustrated to the right. Sketch a graph…

A: Let r be the radius of wheel, r=11 Let y be the height of the bucket above the water.

Q: An ascending space shuttle rises vertically from a launching pad. As it rises the shuttle is tracked…

A: Let us solve the problem in the next step.

Q: Warren boards a Ferris wheel at the 3-o'clock position and rides the Ferris wheel for several…

A:

Q: An observer views a rocket take off from a distance of 6 miles from the launch pad, and tracks the…

A: The given situation can be described by the following figure:

Q: Solve the problem using trigonometric or inverse trigonometric functions. Show illustration, define…

A: The trigonometric ratio gives relation among various side and angles of any right triangle . For a…

Q: A Ferris wheel has a radius of 34.8 feet. The bottom of the Ferris wheel sits 0.7 feet above the…

A: Given: Radius of the Ferris wheel is 34.8 feet. The bottom height is 0.7 feet.

Q: Sine Law A pole tilts towards the sun at an 8 degree angle from the vertical (sun is on the left),…

A: Make a diagram according to the question. Here, AB is the pole and BC is the shadow.

Q: Navigation A boat leaves a port traveling due east at 12 mi>hr. At the same time, another boat…

A: Let the distance travelled by east bound boat at time t be x and the distance travelled by the north…

Q: A rowboat is pushed off from a beach at 8 ft/sec. A man on shore holds a rope, tied to the boat, at…

A: Using derivative we find the rate of change of angle of elevation.

Q: The height above the ground (in meters) of a person on a Ferris wheel as a function of the angle…

A:

Q: A Ferris wheel has a radius of 35 feet. The bottom of the Ferris wheel sits 0.7 feet above the…

A:

Q: Aviation A helicopter maintains an elevation of 3.5 miles and is flying toward a control tower. The…

A: We use Trigonometry ratios

Q: 2000 A television camera at ground level is 2000 feet away from the launching pad of a space rocket…

A:

Q: A 15 ft ladder leans against the side of a house. The top of the ladder is 14 ft off the ground.…

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.