Concept explainers
Willis Tower Willis Tower in Chicago is the second tallest building in the United States and is topped by a high antenna. A surveyor on the ground makes the following measurements
The angle of elevation from his position to the top of the building is
The distance from his position to the top of building is
The distance from his position to the top of antenna is
How far away from the (base of the) building is the surveyor located
How tall is the building
What is the angle of elevation from the surveyor to the top of the antenna
How tall is the antenna
(a)
The distance between the surveyor located and the base of the Willis Tower in
Chicago the tallest building in the United States and is topped by a high antenna.
Answer to Problem 66AYU
Solution:
The distance between the surveyor and the base of the building is approximately
Explanation of Solution
Given information:
A high antenna is mounted on top of the Willis Tower in Chicago, which is the second tallest building in the United States.
The measurements by surveyor on the ground are:
The angle of elevation from the surveyor’s position to the top of the building is
The distance from the surveyor’s position to the top of the building is
The distance from the surveyor’sposition to the top of the antenna is
Explanation:
From the given information, the diagram of the building is as shown below:
In the right angled triangle
adjacent side of the triangle which represents the distance between the surveyor and the base of
the building.
By substituting the values of angle
Therefore, the surveyor is located approximately
(b)
The height of the Willis Tower.
Answer to Problem 66AYU
Solution:
The height of the Willis Tower is
Explanation of Solution
Given information:
A high antenna is mounted on top of the Willis Tower in Chicago, which is the second tallest building in the United States.
The measurements by surveyor on the ground are:
The angle of elevation from the surveyor’s position to the top of the building is
The distance from the surveyor’s position to the top of the building is
The distance from the surveyor’s position to the top of the antenna is
Explanation:
From the given information, the diagram of the building is as shown below:
In the right angled triangle
opposite side of the triangle which represents the height of the building from the ground.
By using the sin ratio in the right triangle
By substituting the values of angle
Therefore, the height of the building from the ground is about
(c)
The angle of elevation from the surveyor to the top of the antenna.
Answer to Problem 66AYU
Solution:
The angle of elevation from the surveyor to the top of the antenna is
Explanation of Solution
Given information:
A high antenna is mounted on top of the Willis Tower in Chicago, which is the second tallest building in the United States.
The measurements by surveyor on the ground are:
The angle of elevation from the surveyor’s position to the top of the building is
The distance from the surveyor’s position to the top of the building is
The distance from the surveyor’s position to the top of the antenna is
Explanation:
From the given information, the diagram of the building is as shown below:
Consider the right angled triangle
to the top of the building.
Here the hypotenuse is
By using the cos ratio in the right triangle
By substituting the values of
Therefore, the angle of elevation from the surveyor to the base of the triangle is
(D)
The height of the antenna
Answer to Problem 66AYU
Solution:
The height of the antenna is
Explanation of Solution
Given information:
A high antenna is mounted on top of the Willis Tower in Chicago, which is the second tallest building in the United States.
The measurements by surveyor on the ground are:
The angle of elevation from the surveyor’s position to the top of the building is
The distance from the surveyor’s position to the top of the building is
The distance from the surveyor’s position to the top of the antenna is
Explanation:
From the given information, the diagram of the building is as shown below:
Consider the right triangle
From part (c), the angle
By using the sin ratio in the right triangle
By substituting the values of
From the diagram
Therefore, the height of the antenna is approximately
Chapter 8 Solutions
Precalculus
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