A plane is flying at a speed of 320 miles per hour on a bearing of N70°E. Its ground speed is 370 miles per hour and its true course is 30°. Find the speed, to the nearest mile per hour, and the direction angle, to the nearest tenth of adegree, of the wind.

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

A: Dot product of two vector 'a' and  'b' is : a→·b→ =|a→|·|b→|*cosθ

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

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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: To estimate the height of a tree to people position himself 35 feet apart. From the first person,…

A:

Q: A straight trail leads from the Alpine Hotel, elevation 8000 feet, to a scenic overlook, elevation…

A: Given: A straight trail leads from the Alpine Hotel, elevation 8000 feet, to a scenic overlook,…

Q: The shafts of an angle drive are acted upon by the two couples shown. Replace the two couples with a…

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Q: A pilot is at an altitude of 3,000 ft, and is 7,060 ft in horizontal distance from the end of the…

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Q: Justin spots a tree directly across the river from where he is standing. He then walks 27 ft…

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Q: A surveyor wishing to find the height of a lighthouse measures the angle A at a point 120 ft. from…

A: Let the height of the light of the lighthouse is h. See the picture below

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: If a plane takes off on runway 38 (N 38° W) and flies 8 miles, then makes a right (90°) turn and…

A: Given that: Takes off at N38°W   and   flies 8 miles and makes right turn 90° and flies 14 miles.…

Q: A communication tower is located at the top of a steephill, as shown. The angle of inclination of…

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Q: A hawk is sitting on top of a tree that is 15 ft. high. It is watching a rabbit that is 18ft. from…

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Q: A hot-air balloon is flying at an altitude of 2685 feet. If the angle of depression from the pilot…

A:

Q: An aeroplane is flying due north but, to avoid a storm, it flies 150 km on a bearing of 060° and…

A: Given,  An aeroplane flying 150 km on a bearing of 060° and then on a bearing of 320° . It done…

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: An observer at the top of a building sees a car on the road below. The angle of depression to the…

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Q: An airplane is observed to be approaching a point that is at a distance of 15 km from the point of…

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

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

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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: The path of a satellite orbiting the earth causes it to pass directly over two tracking stations A…

A: As shown in the figure,A and B are the stations, and D is the satellite.Distance between two…

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

Q: The angle of elevation from a viewer to the center of a fireworks display is 55°. If the viewer is…

A:

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

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Q: The pilot of a small airplane flying 600 m above the ground notices a village 800 horizontal meters…

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Q: Find the angle between v and w to the nearest degree.

A: SOLUTION-

Q: From an airplane at an altitude of 1,289 m, the angle of depression to a rock on the ground measures…

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 small aircraft sets a course with a certain bearing and at a speed of 200 mph. A horizontal wind…

A: The angle θ is 3°

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: The pilot of a small airplane flying 300 m above the ground notices a village off the left wing at a…

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Q: On a bike ride you come to a hill that has a grade of 5%. To the nearest degree, what is the angle…

A: Slope of the hill = tanƟ = 5% = 5 / 100 = 0.05 where Ɵ is  the angle this hill makes with 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: An airship is flying at an altitude of 800 m when it spots a village in the distance with a…

A: Consider the diagram given below, Point A is the location of the plane at that instant, point C is…

Q: An 18 ft. tree casts a 15 ft. long shadow as shown in the following figure. Which of the following…

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

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Q: An observer at the top of a skyscraper sights a tour bus at an angle of depression of 61 degrees.…

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Q: The boat is 3 mi from both light houses and the angle between the line of sight to the lighthouses…

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

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Q: A steamer sails 100 miles due east and then 40 miles on a bearing of 60 degrees.  How far is the…

A: To locate the steamer with respect to distance and the bearing in reference to the starting point

Q: A man climbs 213 meters up the side of a pyramid and finds thatthe angle of depression to his…

A: A man climbs 213 meters up the side of a pyramid and finds that the angle of depression to his…

Q: A mountain cabin is built on the side of a hill with a porch extending over a portion of the…

A: The diagram is shown below:

Q: A man standing between two trees and is 42 feet from the taller tree and 40 feet from the shorter…

A:

Q: A boat is traveling on a bearing of 270°.In what direction was it traveling?

A: The angle measure starts at the positive y-axis (North) Then we have to take 270°. We try to draw it…