Observers at positions A and B 2 km apart simultaneously measure the angle of elevation of a weather balloon to be 40° and 70°, respectively. If the balloon is directly above a point on the line segment between A and B, find the height of the balloon.

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 plane at an elevation of 5.5 km, approaches the airport at an angle of depression of 30°. А 30°…

A: Use the appropriate trigonometric ratio and find out the x.

Q: From an airplane at an altitude of 1200 m, the angle of depression to a rock on the ground measures…

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

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: An aircraft (at Z) is spotted by two observers (at X and Y) who are L = 1750 feet apart. As the…

A: Given: Let XD=x. So, YD=1750-x. In triangle XDZ, ZD=x tan A   and   in triangle ZDY, ZD=(1750-x)…

Q: an airplane is flying from New Orleans to Atlanta. As the airplane is about to finish its course,…

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: A blimp, suspended in the air at a height of 400 feet, lies directly over a line from a sports…

A:

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: To find the distance from a house at point A that is on one side of a river to a house at point B on…

A: As Angle A is 40° and angle C is 50° we get value of angle B is 90°.

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

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

Q: From a helicopter flying at 30,000 feet, the angles of depression of two cities are 28 and 55. How…

A:

Q: An aircraft (at C) is spotted by two observers (at A and B) .o are L=1700 feet apart. As the…

A: Given,           An aircraft at C is spotted by two observersat A and B who are L=1700 feet…

Q: A surveyor stands on a grassland and sees an evergreen tree on the side of a hill. Using their…

A:

Q: A student stands at point A and measures the angle of elevation to the top of a building at 30°. She…

A:

Q: Find the angle of elevation from point C to point A.

A: Given, ∠A=58°, AB=6m,  ∠B= 90°

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: A pilot is flying over a straight highway. He determines the angles of depression to two mileposts,…

A:

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

A:

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

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

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: A plane rises from take-off and flies at an angle of 10° with the horizontal runway. When it has…

A: given,

Q: An aircraft (at Z) is spotted by two observers (at X and Y) who are L=1350 feet apart. As the…

A:

Q: A bird is flying in the sky when it spots a worm on the ground. If the angle of depression from the…

A:

Q: A kite is flying at an angle of elevation of 43 degrees. Find the height of the kite if 37 ft of the…

A:

Q: . When you look up at an object, the acute angle measuredfrom the horizontal to a line-of-sight…

A: When you look up at an object, the acute angle measured from the horizontal to a line-of-sight…

Q: A Navy battleship is targeting an incoming fighter jet with an elevation of 10,000 feet. The…

A:

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

A: SOLUTION-

Q: d) A helicopter is hovering above a road at an altitude of 24 m. At a certain time, the horizontal…

A: given: A helicopter above a road at an altitude of 24 m. Distance between the car and the helicopter…

Q: A plane at an elevation of 5.5 km, approaches the airport at an angle of depression of 30°. A 30°…

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: 2. Viola drives 170 meters up a hill that makes an angle of 6° with the horizontal. To the nearest…

A:

Q: 2. Sketch a diagram of any angle in standard position terminating in quadrant II, that has the point…

A: topic - cartesian plane

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

A:

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

A:

Q: Drag the yellow dot until AC and DF are exactly parallel. Afterwards, use the protractor to measure…

A:

Q: An aircraft (at Z) is spotted by two observers (at X and Y) who are L = 2000 feet apart. As the…

A: Given that the total length XY = L = 2000 feet and the angle A = 40 degree and angle B = 20 degree.…

Q: Figure 17 shows a walkway with a handrail. Angle a is the angle between the walkway andthe…

A:

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: An aircraft (at Z) is spotted by two observers (at X and Y) who are L= 1850 feet apart. As the…

A: SOLUTION-

Q: Determine the horizontal distance from point A to each mountain peak. 2. State a position vector for…

A:

Q: A ________ measures the acute angle that a path or line of sight makes with a fixed north-south line

A: A Bearing measures the acute angle that a path or line of sight makes with a fixed north-south line.

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.