The boat is 3 mi from both light houses and the angle between the line of sight to the lighthouses is 20°. Find the distance between the lighthouses.

Q: A mother gazes out a second-floor window at her son playing at the playground. If the mother's eye…

A: The arrangement of mother's eye level, ground level and playground forms a right angles triangle.…

Q: A passenger lift runs 680 ft up the side of a mountain from the base to an exit station. If the…

A:

Q: From a window 30 feet above the level ground, a building 100 feet high, and at a distance of 200…

A:

Q: When the direction of the sun makes an angle of 35.2° with the horizontal, an oil derrick casts a…

A: When the direction of the sun makes an angle of 35.2° with the horizontal, an oil derrick casts a…

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: Nico is resting on a 3m high tree house and watching the top of a pole 5m from the tree. if the…

A:

Q: An observer is 120 ft from the base of a television tower, which is 150 ft tall. Find the angle of…

A: Given query is to find the angle of elevation.

Q: Please help me find angle C

A: To calculate the angle C in the given right-angled triangle ABC.

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

A:

Q: If you stand 35 feet from the bottom of a movie screen and the screen is 75 feet tall, what is the…

A: If you stand 35 feet from the bottom of a movie screen. The screen is 75 feet tall its make a…

Q: A lighthouse is 20 feet tall, and a boat is 50 feet from the base of the lighthouse. What is the…

A:

Q: A ranger in a 95 ft tower looks down at an angle of depression of 49 and spots a camper in trouble.…

A:

Q: A pilot is flying over a flat (horizontal) land. She determines the angle of depression to a…

A: The given situation is as shown. Now, use the fact that sum of the angle s of the triangle is 180°.…

Q: A ship sailing parallel to shore sights a lighthouse at an angle of 20° from its direction of…

A: Given a ship sailing parallel to shore sighta lighthouse at an angle of 20°

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

A:

Q: Suppose you are headed toward a plateau 63m high. If the angle of elevation to the top of the…

A: Suppose you are headed toward a plateau 63m high. The angle of elevation to the top of the plateau…

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: You are in a tall building and from your window you notice a window washer working on the building…

A:

Q: From a hot air balloon 2,500 feet above the ground, you see a clearing whose angle of depression is…

A: The height is 2,500 feet above the ground. The angle of depression is 25°

Q: The Tower of Terror ride in Disney World, Florida is 199 feet tall. If Josh is standing 132 feet…

A: Given: The Tower of Terror ride in Disney World, Florida is 199 feet tall. If Josh is standing 132…

Q: The angle elevation to the top building in Chicago is found to be 9 degrees from the ground at a…

A:

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: A ship is on the surface of the water, and its radar detects a submarine at a distance of 238 ft, at…

A: Here we have to use basic trigonometric ratios to find the depth of the submarine.

Q: A water main is to be constructed with a 20% grade in the north direction and a 10% grade in the…

A: A water main is to be constructedwith a 20% grade in the north direction and a 10% grade in the east…

Q: A water main is to be constructed with a 10% grade in the north direction and a 20% grade in the…

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: Find the angle β in the fourth quadrant such that sec⁡ β =2, where 0°≤ β ≤360° .

A:

Q: Due to a storm, a pilot flying at an altitude of 586 feet has to land early. If he has a horizontal…

A:

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: A water main is to be constructed with a 12.5% grade in the north direction and a 20​% grade in the…

A: Known result:

Q: A telephone pole in Valdosta casts no shadow at the same time as a telephone pole in Atlanta casts a…

A: Given A telephone pole in Valdosta casts no shadow And at the same time as a telephone pole in…

Q: The angle of elevation from the top of a small building to the top of a nearby taller building is…

A: Given angle of elevation 46° Angle of depression 14°

Q: Jazmin is flying a kite, but it got caught at the top of a 24 ft tree. If she let out 100 ft of…

A:

Q: . The Sears Tower in Chicago is 1454 feet tall and is situated about 1 mile inland from the shore of…

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 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: From a building across the street, the angle of depression of the foot of an edifice is measured as…

A:

Q: A billboard, 54 feet wide, is prependicular to a staright road and is 18 feet from the nearest point…

A:

Q: From the top of a lighthouse was 60 m above sea level. A ship located 1200 m from the shore could…

A: Given:   To determine: angle of depression θ

Q: O A woman 1.65 m tall stood 50 m away from the foot of a tower and observed that the angle of…

A: Solution: The objective is to find the height of the tower

Q: An observer saw a canoe 8 meters below the cliff that makes a viewing angle with respect to the…

A: Given conditions can be drawn as follows, Here, Angle of depressions 30o and angle ABC are…

Q: A 3000-lb car traveling uphill has a grade resistance of 150 lb. Find the angle of the grade to the…

A: Given: A 3000-lb car traveling uphill has a grade resistance of 150 lb.

Q: The angle of depression from a helicopter to a landing pad is 65 degrees. If the horizontal distance…

A: Given that  The angle of depression from a helicopter to a landing pad is 65 degrees horizontal…

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

A:

Q: A large weather balloon is tethered by two ropes. The shorter rope is measures 20 feet and attaches…

A: The shorter rope is measures 20 feet and attaches to the balloon at an angle of 32 degrees from the…

Q: a hot air balloon at a 35° angle of elevation. 7) Lee, on the ground, looks up at Bruce If lee and…

A:

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: Suppose your angle of elevation to the top of a water tower is 78°. If the water tower is 145 ft…

A: Here we will use the concept of trigonometry and find the solution. We have to find the distance…

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.