Precalculus
Precalculus
9th Edition
ISBN: 9780321716835
Author: Michael Sullivan
Publisher: Addison Wesley
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Chapter 8.1, Problem 66AYU

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 34 .

The distance from his position to the top of building is 2595 feet.

The distance from his position to the top of antenna is 2760 feet.

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)

Expert Solution
Check Mark
To determine

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 2151 feet.

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 34.

The distance from the surveyor’s position to the top of the building is 2595 feet.

The distance from the surveyor’sposition to the top of the antenna is 2760 feet.

Explanation:

From the given information, the diagram of the building is as shown below:

Precalculus, Chapter 8.1, Problem 66AYU , additional homework tip  1

In the right angled triangle BCD, an angle B is 34 and the hypotenuse is 2595ft and BC is the

adjacent side of the triangle which represents the distance between the surveyor and the base of

the building.

BC is found by using cos ratio in the right triangle BCD,

cos(B)=BCBD

By substituting the values of angle B=34 and BD=2595, it gives,

cos(34)=BC2595

BC=2595cos(34)

BC=2151.352502151ft

Therefore, the surveyor is located approximately 2151 feet from the base of the building.

(b)

Expert Solution
Check Mark
To determine

The height of the Willis Tower.

Answer to Problem 66AYU

Solution:

The height of the Willis Tower is 1451 feet.

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 34.

The distance from the surveyor’s position to the top of the building is 2595 feet.

The distance from the surveyor’s position to the top of the antenna is 2760 feet.

Explanation:

From the given information, the diagram of the building is as shown below:

Precalculus, Chapter 8.1, Problem 66AYU , additional homework tip  2

In the right angled triangle BCD, angle B is 34 and the hypotenuse is 2595ft and DC is the

opposite side of the triangle which represents the height of the building from the ground.

By using the sin ratio in the right triangle BCD,

sin(B)=CDBD

By substituting the values of angle B=34 and BD=2595, it gives,

sin(34)=CD2595

CD=2595sin(34)

CD=1451.10561451ft

Therefore, the height of the building from the ground is about 1451 feet.

(c)

Expert Solution
Check Mark
To determine

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 38.8.

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 34.

The distance from the surveyor’s position to the top of the building is 2595 feet.

The distance from the surveyor’s position to the top of the antenna is 2760 feet.

Explanation:

From the given information, the diagram of the building is as shown below:

Precalculus, Chapter 8.1, Problem 66AYU , additional homework tip  3

Consider the right angled triangle BCA, the angle B is the angle of elevation from the surveyor

to the top of the building.

Here the hypotenuse is 2760ft and by the subpart a the adjacent side BC is 2151ft.

By using the cos ratio in the right triangle BCA,

cos(B)=BCAB

By substituting the values of BC=2151 feet, AB=2760 feet,

cos(B)=21512760=0.77935

B=cos1(0.77935)=38.8

Therefore, the angle of elevation from the surveyor to the base of the triangle is 38.8.

(D)

Expert Solution
Check Mark
To determine

The height of the antenna

Answer to Problem 66AYU

Solution:

The height of the antenna is 278 feet.

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 34.

The distance from the surveyor’s position to the top of the building is 2595 feet.

The distance from the surveyor’s position to the top of the antenna is 2760 feet.

Explanation:

From the given information, the diagram of the building is as shown below:

Precalculus, Chapter 8.1, Problem 66AYU , additional homework tip  4

Consider the right triangle BCA, AD represents the antenna.

From part (c), the angle B=38.8.

By using the sin ratio in the right triangle BCA,

sin(B)=ACAB

By substituting the values of B=38.8 and AB=2760, it gives,

sin(B)=AC2760.

sin(38.8)=AC2760

CA=sin(38.8)2760

AC=1729.42651729.43 feet.

From the diagram AC=AD+DC

AD=AC-DC

AC=1729.43 feet, and from part b, DC=1451 feet.

AD=1729.43-1451=278.43278

Therefore, the height of the antenna is approximately 278 feet.

Chapter 8 Solutions

Precalculus

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Ch. 8.3 - In Problems 17-32, solve each triangle. a=4 , b=5...Ch. 8.3 - In Problems 17-32, solve each triangle. a=2 , b=2...Ch. 8.3 - In Problems 17-32, solve each triangle. a=3 , b=3...Ch. 8.3 - In Problems 1732, solve each triangle....Ch. 8.3 - In Problems 17-32, solve each triangle. a=4 , b=3...Ch. 8.3 - In Problems 17-32, solve each triangle. a=10 , b=8...Ch. 8.3 - In Problems 17-32, solve each triangle. a=9 , b=7...Ch. 8.3 - In Problems 33-42, solve each triangle using...Ch. 8.3 - In Problems 33-42, solve each triangle using...Ch. 8.3 - In Problems 33-42, solve each triangle using...Ch. 8.3 - Prob. 36AYUCh. 8.3 - Prob. 37AYUCh. 8.3 - In Problems 33-42, solve each triangle using...Ch. 8.3 - Prob. 39AYUCh. 8.3 - Prob. 40AYUCh. 8.3 - Prob. 41AYUCh. 8.3 - Prob. 42AYUCh. 8.3 - Distance to the Green A golfer hits an errant tee...Ch. 8.3 - Navigation An airplane flies due north from Ft....Ch. 8.3 - Avoiding a Tropical Storm A cruise ship maintains...Ch. 8.3 - Revising a Flight Plan In attempting to fly from...Ch. 8.3 - Major League Baseball Field A major league...Ch. 8.3 - Little League Baseball Field According to Little...Ch. 8.3 - Finding the Length of a Guy Wire The height of a...Ch. 8.3 - Finding the Length of a Guy Wire A radio tower 500...Ch. 8.3 - Prob. 51AYUCh. 8.3 - Prob. 52AYUCh. 8.3 - Prob. 53AYUCh. 8.3 - Prob. 54AYUCh. 8.3 - Prob. 55AYUCh. 8.3 - Prob. 56AYUCh. 8.3 - Prob. 57AYUCh. 8.3 - Prob. 58AYUCh. 8.3 - Prob. 59AYUCh. 8.3 - Prob. 60AYUCh. 8.3 - Prob. 61AYUCh. 8.3 - Prob. 62AYUCh. 8.3 - Prob. 63AYUCh. 8.4 - The area K of a triangle whose base is b and whose...Ch. 8.4 - If two sides a and b and the included angle C are...Ch. 8.4 - The area K of a triangle with sides a , b , and c...Ch. 8.4 - Prob. 4AYUCh. 8.4 - Prob. 5AYUCh. 8.4 - Prob. 6AYUCh. 8.4 - Prob. 7AYUCh. 8.4 - Prob. 8AYUCh. 8.4 - Prob. 9AYUCh. 8.4 - Prob. 10AYUCh. 8.4 - Prob. 11AYUCh. 8.4 - Prob. 12AYUCh. 8.4 - Prob. 13AYUCh. 8.4 - Prob. 14AYUCh. 8.4 - Prob. 15AYUCh. 8.4 - Prob. 16AYUCh. 8.4 - Prob. 17AYUCh. 8.4 - Prob. 18AYUCh. 8.4 - Prob. 19AYUCh. 8.4 - Prob. 20AYUCh. 8.4 - Prob. 21AYUCh. 8.4 - Prob. 22AYUCh. 8.4 - Prob. 23AYUCh. 8.4 - Prob. 24AYUCh. 8.4 - Prob. 25AYUCh. 8.4 - Prob. 26AYUCh. 8.4 - Prob. 27AYUCh. 8.4 - Prob. 28AYUCh. 8.4 - Prob. 29AYUCh. 8.4 - Prob. 30AYUCh. 8.4 - Prob. 31AYUCh. 8.4 - Prob. 32AYUCh. 8.4 - Prob. 33AYUCh. 8.4 - Prob. 34AYUCh. 8.4 - Cost of a Triangular Lot The dimensions of a...Ch. 8.4 - Prob. 36AYUCh. 8.4 - Prob. 37AYUCh. 8.4 - Prob. 38AYUCh. 8.4 - Prob. 39AYUCh. 8.4 - Prob. 40AYUCh. 8.4 - Prob. 41AYUCh. 8.4 - Prob. 42AYUCh. 8.4 - Prob. 43AYUCh. 8.4 - Prob. 44AYUCh. 8.4 - Prob. 45AYUCh. 8.4 - Prob. 46AYUCh. 8.4 - Prob. 47AYUCh. 8.4 - Prob. 48AYUCh. 8.4 - Prob. 49AYUCh. 8.4 - Prob. 50AYUCh. 8.4 - Prob. 51AYUCh. 8.4 - Prob. 52AYUCh. 8.4 - Prob. 53AYUCh. 8.4 - Prob. 54AYUCh. 8.4 - Prob. 55AYUCh. 8.4 - Prob. 56AYUCh. 8.5 - The amplitude A and period T of f( x )=5sin( 4x )...Ch. 8.5 - Prob. 2AYUCh. 8.5 - Prob. 3AYUCh. 8.5 - Prob. 4AYUCh. 8.5 - Prob. 5AYUCh. 8.5 - Prob. 6AYUCh. 8.5 - Prob. 7AYUCh. 8.5 - Prob. 8AYUCh. 8.5 - Rework Problem 7 under the same conditions, except...Ch. 8.5 - Prob. 10AYUCh. 8.5 - Rework Problem 9 under the same conditions, except...Ch. 8.5 - Rework Problem 10 under the same conditions,...Ch. 8.5 - Prob. 13AYUCh. 8.5 - Prob. 14AYUCh. 8.5 - Prob. 15AYUCh. 8.5 - Prob. 16AYUCh. 8.5 - In Problems 15-22, the displacement (in meters) of...Ch. 8.5 - Prob. 18AYUCh. 8.5 - Prob. 19AYUCh. 8.5 - Prob. 20AYUCh. 8.5 - Prob. 21AYUCh. 8.5 - Prob. 22AYUCh. 8.5 - Prob. 23AYUCh. 8.5 - Prob. 24AYUCh. 8.5 - Prob. 25AYUCh. 8.5 - Prob. 26AYUCh. 8.5 - Prob. 27AYUCh. 8.5 - Prob. 28AYUCh. 8.5 - Prob. 29AYUCh. 8.5 - Prob. 30AYUCh. 8.5 - Prob. 31AYUCh. 8.5 - Prob. 32AYUCh. 8.5 - Prob. 33AYUCh. 8.5 - Prob. 34AYUCh. 8.5 - Prob. 35AYUCh. 8.5 - Prob. 36AYUCh. 8.5 - Prob. 37AYUCh. 8.5 - Prob. 38AYUCh. 8.5 - Prob. 39AYUCh. 8.5 - Prob. 40AYUCh. 8.5 - Prob. 41AYUCh. 8.5 - Prob. 42AYUCh. 8.5 - Prob. 43AYUCh. 8.5 - Prob. 44AYUCh. 8.5 - Prob. 45AYUCh. 8.5 - Prob. 46AYUCh. 8.5 - Prob. 47AYUCh. 8.5 - In Problems 45-50. the distance d (in meters) of...Ch. 8.5 - Prob. 49AYUCh. 8.5 - Prob. 50AYUCh. 8.5 - Loudspeaker A loudspeaker diaphragm is oscillating...Ch. 8.5 - Colossus Added to Six Flags St. Louis in 1986, the...Ch. 8.5 - Tuning Fork The end of a tuning fork moves in...Ch. 8.5 - Tuning Fork The end of a tuning fork moves in...Ch. 8.5 - Charging a Capacitor See the illustration. 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