A hot-air balloon is floating above a straight road. To estimate their height above the ground, the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be 22° and 24°. How high is the balloon?

Q: A 200-foot cliff drops vertically into the ocean. If the angle of elevation from a ship to the top…

A: Let the distance of the ship offshore is x feet. A rough sketch of given situation is shown below…

Q: A dog looks up at a cat who has climbed a 29 foot tree. If the dog is 59 feet from the base of the…

A: The relation between the angles of a triangle and the sides of the triangle is given by the…

Q: An air traffic controller on top of a 300-foot airport tower looks up and sees a balloon. The angle…

A: An air traffic controller on top of a 300-foot airport tower looks up and sees a ballon.The angle of…

Q: From a window 30 feet above the street, the angle of depression of the curb on the near side of the…

A:

Q: A kite is flying at an angle of elevation of 67° with the ground. If 100 feet of string have been…

A:

Q: On a test flight, during the landing of the space shuttle, the ship was 366 ft above the end of the…

A:

Q: Find the angle that an 18-foot ladder leaning against a wall makes with the ground If the bottom of…

A:

Q: An airplane is flying 5000 feet above the ground. If the angle of depression to the airport runway…

A: Use tan theta to calculate ground distance

Q: At 11:30 A.M. the angle of elevation of the sun for Washington, D.C., is 55.7°. If the height of the…

A:

Q: A boy flying his kite releases the entire length of his string which measures 21 m, so that the kite…

A:

Q: A ranger at the top of a fire tower observes the angle of depression to a fire on level ground to be…

A: From the given problem the representative diagram is as shown below.

Q: Find the angle that an 18-foot ladder leaning against a wall makes with the ground if the bottom of…

A: Here use we have to use trigonometric ratio to find the angle required.

Q: After a hurricane, a homeowner examines trees on his property for damage. He thinks a 21-ft palm…

A: After a hurricane, a homeowner examines trees and thinks a 21-ft palm tree is leaning slightly from…

Q: A satellite orbiting the earth passes directly overhead at observation stations in Phoenix and Los…

A:

Q: Bob, who is 2.2 m tall, is standing a distance of 15 m from a flagpole as shown below. From his…

A:

Q: A kite flies to a height of 35 feet when 74 feet of string is out. If the string is in a straight…

A:

Q: what is the height of the house (opposite side of the triangle)?

A:

Q: A surveyor in an airplane travelling east sees a lake in front of her. The angle of depression to…

A:

Q: A kite flies at a height of 35 feet when 60 feet of string is out.If the string is in a straight…

A: We have, a kite flies at a height of 35 feet when 60 feet of string is out and the string is in a…

Q: Kurt spots a bird sitting at the top of a 40ft tall telephone pole. If the angle of elevation from…

A: Let x be the distance between Kurt and base of the pole. Now the diagrammatic representation of the…

Q: At a spot 400 feet from the base of a building the angle of elevation to the bottom of a flag pole…

A: To find height of flagpole

Q: A building 150 feet tall casts a 30 foot long shadow. If a person looks down from the top of the…

A: Given,

Q: An observer on the roof of Building A measures a 27° angle of depression between the horizontal and…

A:

Q: A kite is 50 feet high when 170 feet of string is out. What angle does the kite make with the ground…

A:

Q: A telephone company is building a 30-foot antenna to carry cell phone transmissions. As shown in the…

A:

Q: From a hotel window 30 meters above the ground, Alan finds that the angle of elevation of the top of…

A: Let the distance between the monument and the hotel window be x. Then we get,…

Q: A man is standing on the ground, looking at the top of an 80-ft building. The angle of elevation is…

A:

Q: A 16 foot ladder leaning against a wall of a house makes a 50 degree angle with the ground. How far…

A: We can find the answer as below

Q: A boy flying his kite releases the entire length of his string which measures 26 m, so that the kite…

A: Find the solution below

Q: A 300-foot tall monument is located in the distance. From a window in a building, a person…

A:

Q: A kite flies at a height of 30 feet when 65 feet of string is out. If the string is in a straight…

A: Given: A kite flies at a height of 30 feet when 65 feet of string is out. The figure gives the clear…

Q: A hot-air balloon is floating above a straight road. To estimate their height above the ground, the…

A:

Q: A person standing on the street looks up to the top of a building and finds the angle of elevation…

A: Given that the person is standing near the building

Q: A surveyor set up his instrument at A and measured the angle of elevation of the top of a tower and…

A:

Q: At 11:30 a.m. the angle of elevation of the sun for one city is 55.9°. If the height of a monument…

A:

Q: A radio tower is located 350 feet from a building. From a window in the building, a person…

A:

Q: A man wants to determine the height of a light house. He measured the angle from the ground and…

A: Given   tan A=3/4 Distance from base of light house to A is 40m .  We have to find height of light…

Q: A 16 foot ladder leaning against a wall of a house makes a 50∘angle with the ground. How far up the…

A:

Q: If you have a 16-ft extension ladder, and you place it against a wall so that it has a 35-degree…

A:

Q: Two boats are traveling toward a lighthouse that is 200 feet (ft) above sea level at its top. When…

A:

Q: A 16 foot ladder is used to scale a 14.5 foot wall. At what angle of elevation must the ladder be…

A: Please see the answer below.

Q: The angle of elevation to the top of a building is 38 . From a point 440 ft. farther away the angle…

A:

Q: in a building, a person determines that the angle of elevation to the top of the monument is 15° and…

A:

Q: An Air Force pilot making a preliminary aerial survey, first observed that when he flew directly…

A: Question:An Air Force pilot making a preliminary aerial survey, first observed that when he flew…

Q: A man is lying on the beach, flying a kite. He holds the end of the kite string at ground level and…

A: Man holds the end of the kite string at ground level and estimates the angle of elevation of the…

Q: A man is lying on the beach, flying a kite. He holds the end of the kite string at ground level, and…

A: Let the angle of elevation be 'θ' and the length of the string be 'x'. Let the height of the kite…

Q: A hot-air balloon is floating above a straight road. To estimate their height above the ground, the…

A:

Q: A hot air balloon is floating above a straight road. To estimate their height above the ground, the…

A: Here we will find height of balloon from the ground,

Q: A hot-air balloon is floating above a straight road. To calculate their height above the ground, the…

A: Given that a hot-air balloon is floating above a striaght road angles of depression are 21° and 23°…

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.