The maximum distance that one can see from the observation deck of the Toronto CN tower.

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.2, Problem 100E
To determine

The maximum distance that one can see from the observation deck of the Toronto CN tower.

Expert Solution

The maximum distance that one can see from the observation deck of the Toronto CN tower is 2.18×105ft_.

Explanation of Solution

Formula used:

D=2rh+h2

Where D is the maximum distance that can be seen from the top of a tall building, h is the height of the building, r is the radius of the earth.

Calculation:

Given that, the radius of the earth is 3960 mi and the height of the observation deck of the Toronto CN Tower is 1135 ft.

It is known that, 1mi=5280ft.

Use the unit conversion to convert the distance 3960mi into feet as shown below.

3960mi=3960×1mi=3960×5280ft=20908800ft

Therefore, the radius of the earth is 20908800ft.

Substitute 20908800ft for r, 1135ft for h in the formula to calculate D as follows.

D=2×(20908800ft)×(1135ft)+(1135ft)2=47462976000+1288225ft=47464264225ft=217862.948ft

Now, move decimal 5 places to the left and write 5 as power of 10 to express the above quantity in proper scientific notation.

D=217862.948ft=2.17862948×105ft

Round off the above quantity up to 2 decimal places as shown below.

D=2.17862948×105ft=2.18×105ft

Therefore, the maximum distance that one can see from the observation deck of the Toronto CN tower is 2.18×105ft_.

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