Answered: Height of a Hill A road up a hill makes…

Height of a Hill A road up a hill makes an angle of 5 degree with the horizontal. If theroad from the bottom of the hill to the top of the hill is 2.5 miles long, how high isthe hill?

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter5: Trigonometric Functions: Right Triangle Approach

Section5.2: Trigonometry Of Right Triangles

Problem 60E: Determining a Distance A woman standing on a hill sees a flagpole that she knows is 60 ft tall. The...

See similar textbooks

Related questions

Q: angle of elevation from point A on the ground to the top of a 225-foot cell phone tower is 65°.…

Q: A kite's string is 25 feet long. The angle of elevation of the string of the kite is 32°. If a…

A: To find the height of the kite

Q: Height of an Obelisk Two people decide to find the height of an obelisk. They posi-tion themselves…

A: In △ABC, tan 65∘=hxh=x tan 65∘ (1) In △ABD, tan 54∘=h25+xh=tan 54∘25+x (2)

Q: Watering a Lawn A water sprinkler sprays water over adistance of 30 feet while rotating through an…

A: θ=135° & r=30 Now area of the sector is, A=θ360°·πr2=135°360°·π302=1060.2875 ft2

Q: A 17ft ladder on ground level is leaning againist a house. If the ladder's angle of elevation is 63…

Q: Height of a building From a point A that is 8.20 meters above level ground, the angle of elevation…

A: The point A is 8.20 m above the ground level. Let PQ be the building. A rough sketch for the…

Q: You are climbing a mountain by the steepest route at a slope of 25∘ when you come upon a trail…

A: The steepest route at a slope of 25°.Then we start the branch trail, the angle is 45°

Q: Speed of an airplane An airplane flying at an altitude of 10,000 feet passes directly over a fixed…

A: Definition used- Speed of plane V=Altitutdetan (Angle of…

Q: A tree is observed on the opposite bank of a river. At a point the river is known to be 120 feet…

Q: Height A ladder that is 20 feet long leans against theside of a house. The angle of elevation of the…

A: Height A of the ladder that is 20 feet long It leans against the side of a house. The angle of…

Q: The angle of elevation to the top of a skyscraper from a 30m high house is 50 degrees. The base of…

Q: Distance between Runners Two runners in a marathondetermine that the angles of elevation of a news…

A: Two runners in a marathon, the angles of elevation of a news helicoptercovering the race are 38° and…

Q: Height of a kite A person flying a kite holds the string 4 feet above ground level. The string of…

A: Given, the string of a kite is 4 feet above the ground level. Also, the string makes an angle 60°…

Q: Height of a Building The angle of elevation to the top of theEmpire State Building in New York is…

A: Suppose that: The height of the Empire State Building = x Note: 1 mi = 5280…

Q: Height of a tower From a point P on level ground, the angle of elevation of the top of a tower is…

A: Refer the illustrative figure below.

Q: Altitude of a rocket A rocket is fired at sea level and climbs at a constant angle of 75° through a…

A: The diagram for this problem is as shown below.

Q: Height of a Hill A road up a hill makes an angle of 6.58 with the horizontal. If the roadfrom the…

A: According to the given question the figure is as follows,

Q: 9.8 ft 59°

Q: A tree is observed on the opposite bank of a river. At that point the river is known to be 140 feet…

Q: Distance A hot-air balloon is held at a constant altitude by two ropes that areanchored to the…

A: To Determine: What is the distance between the points on the ground at which the two ropes are…

Q: You are at the airport and observing airplanes. You are watching an airplane approaching the…

A: Given You are at the airport and observing airplanes. You are watching an airplaneapproaching the…

Q: plane rises from take-off and flies at an angle of 6° with the horizontal runway. When it has gained…

Q: Airplane Ascent An airplane leaves the runway climbingat an angle of 18° with a speed of 275 feet…

A: Given : Airplane Ascent An airplane leaves the runway climbing at an angle of 18° with a speed of…

Q: A kite string is 200 meters long. Find the height of the kite if the string makes an angle of…

Q: A tree grows at an angle of 4 degrees from the vertical due to prevailing winds. At a point 40…

Q: Height of a Mountain While traveling across flat land,you notice a mountain directly in front of…

Q: Height of a Mountain To estimate the height of amountain above a level plain, the angle of elevation…

A: Definition used - In a right angle triangle -…

Q: Distance An airplane flying at an altitude of 6 miles is on a flight path that passesdirectly over…

A: Consider the following labels on the diagram: (a) When θ=30°, then, in right-angled triangle OAB,…

Q: A boat is heading towards a lighthouse, whose beacon-light is 107 feet above the water. From point…

A: Given: Height of lighthouse, h=107 ft Angle of elevation of beacon from AA = 12o BB= 20o

Q: bird

Q: . Elevation of a Kite A man is lying on the beach, flyinga kite. He holds the end of the kite string…

A: Given that ; The angle of elevation of the kite is 50° . The string is 450 ft long .

Q: A truck travels 12 km up a mountain road. The change in height from the bottom to the top is 732 m.…

A: topic - trigonometric ratios

Q: A 16 ft ladder leans agalnst the side of a house. The top of the ladder Is 15 ft off the ground.…

Q: Height of Cloud Cover To measure the height of the cloud cover at an airport, a worker shines a…

Q: Height of a Building A man standing on the roof of a building 60.0 feet high looksdown to the…

A: Let AB = First building, CD = building next door and BD = distance between them.

Q: ships leave a harbor entrance at the same time. The first ship is traveling at a constant 18 miles…

Q: A fire ranger stands at an observation window 70 ft above the ground. She sees a fire in the…

A: Consider

Q: A ladder leans agalnst the slde of a house. The angle of elevation of the ladder Is 61°, and the top…

A: Given that the angle of elevation of the ladder is 61° and the top of the ladder is 13 ft above the…

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

A: Find the horizontal distance

Q: A sailboat leaves st. Thomas bound for an island in the British West Indies 200 miles away…

A: According to the given scenario, we draw the figure like The sailboat started from point A and…

Q: Radio Antenna A short-wave radio antenna is supported bytwo guy wires, 165 ft and 180 ft long. Each…

A: Radio Antenna A short-wave radio antenna is supported bytwo guy wires, 165 ft and 180 ft long. Each…

Q: 17. You are lost at sea. A helicopter has come to rescue you. The helicopter is flying at a height…

A: Introduction: The angle of depression and the angle of elevation are related to trigonometry. When a…

Q: Sun's elevation Approximate the angle of elevation a of the sun if a person 5.0 feet tall casts a…

A: Given, If a person 5 feet tall cast a shadow 4 feet long on the ground, Find the approximate…

Q: visitor at an art gallery sits on the floor, 2.4 m from the wall, and looks up at a painting. He can…

Q: Directions: Draw a picture torepresent the situation. Then, solve the problem. You must show all of…

A: Given that: Length of shadow: s=6 mAngle of elevation from the tip of the shadow to the top of the…

Q: Leaning Ladder A 20-ft ladder leans against a building sothat the angle between the ground and the…

A: Given that : Ladder length = 20 ft and angle between the ground and the ladder is 72° .

Q: A 15th ladder leans against the side of a house. The bottom of the ladder is a 6 ft away from the…

Q: Angle of Elevation A woman entering an outside glass elevator on the ground floorof a hotel glances…

Q: On a hill, inclined at an angle of 19 with the horizontal , stand a mango tree. At a point A 25…

Q: A ship receives sonar reflections at an angle of depression of 31° from a submarine 27 km above the…

A: Topic - trigonometry

Concept explainers

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.

Question

Height of a Hill A road up a hill makes an angle of 5 degree with the horizontal. If the
road from the bottom of the hill to the top of the hill is 2.5 miles long, how high is
the hill?

Figure in plane geometry formed by two rays or lines that share a common endpoint, called the vertex. The angle is measured in degrees using a protractor. The different types of angles are acute, obtuse, right, straight, and reflex.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Ratios$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.

Similar questions

Leaning Ladder A 20-ft ladder is leaning against a building. If the base of the ladder is 6 ft from the base of the building, what is the angle of elevation of the ladder? How high does the ladder reach on the building?
Height of a Tower A 600-ft guy wire is attached to the top of a communications tower. If the wire makes an angle of 65 with the ground, how tall is the communications tower?
Height of a Tree A tree on a hillside casts a shadow 215 ft down the hill. If the angle of inclination of the hillside is 22 to the horizontal and the angle of elevation of sun is 52, find the height of the tree.
Height of a Tower A water tower is located 325 ft from a building see the figure. From a window in the building, an observer notes that the angle of elevation to the top of the tower is 39 and that the angle of depression to the bottom of the tower is 25. How tall is the tower? How high is the window?
Height of a Building From a point A on the ground, the angle of elevation to the top of a tall building is 24.1. From a point B, which is 600 ft closer to the building, the angle of elevation is measured to be 30.2. Find the height of the building.
Tracking a Satellite The path of a satellite orbiting the earth causes the satellite to pass directly over two tracking stations A and B, which are 50 mi apart. When the satellite is on one side of the two stations, the angles of elevation at A and B are measured to be 87.0 and 84.2 respectively. a How far is the satellite from station A? b How high is the satellite above the ground?
Height of a Mountain In traveling across flat land, you see a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5. After you drive 13 miles closer to the mountain, the angle of elevation is 9 (see figure). Approximate the height of the mountain.
Determining a Distance A woman standing on a hill sees a flagpole that she knows is 60 ft tall. The angle of depression to the bottom of the pole is 14, and the angle of elevation to the top of the pole is 18, Find her distance x from the pole.
Angle of Elevation A man standing near a building notices that the angle of elevation to the top of the building is 64. He then walks 240 ft farther away from the building and finds the angle of elevation to the top to be 43. How tall is the building?
Leaning Windmill After a wind storm, a farmer notices that his 32-foot windmill may be leaning, but he is not sure. From a point on the ground 31 feet from the base of the windmill, he finds that the angle of elevation to the top of the windmill is 48. Is the windmill leaning? If so, what is the acute angle the windmill makes with the ground?
Height of a Flagpole Two people decide to estimate the height of a flagpole. One person positions himself due north of the pole and the other person stands due cast of the pole. If the two people are the same distance from the pole and 25 feet from each other, find the height of the pole if the angle of elevation from the ground to the top of the pole at each persons position is 56 (Figure 21). Figure 21
Distance An observer in a lighthouse 350 feet above sea level observes two ships directly offshore. The angles of depression to the ships are 4 and 6.5 (see figure). How far apart are the ships?