# Distance A Person Can See From Deck

#### harpazo

##### Full Member
Section R.3
Geometry Essentials
Michael Sullivan
Textbook: College Algebra Edition 9

The deck of a destroyer is 100 feet above sea level. How far can a person see from the deck?

A similar question (using different numbers) found online provided the following information:

"The mathematically correct formula is d^2 = 2*r*h where d is the distance to the horizon, r is the radius of the earth, and h is the height above sea level, all in the same units."

Hint Provided by Sullivan:

I basically plug and chug.

d^2 = 2(3690)(100)

d^2 = 792,000

sqrt{d^2} = sqrt{792,000}

d = 889.9438184515

A person standing on the deck of a destroyer 100 feet above sea level can see about 889.94 feet. What do you say?

#### Dr.Peterson

##### Elite Member
"The mathematically correct formula is d^2 = 2*r*h where d is the distance to the horizon, r is the radius of the earth, and h is the height above sea level, all in the same units."

Hint Provided by Sullivan:

...
A person standing on the deck of a destroyer 100 feet above sea level can see about 889.94 feet. What do you say?
Check your units! Are your r and h given in the same units?

Also, does the answer make sense?

I assume Sullivan gave the same equation to use? It would be helpful to quote the entire problem exactly, rather than refer to a different source.

#### harpazo

##### Full Member
Check your units! Are your r and h given in the same units?

Also, does the answer make sense?

I assume Sullivan gave the same equation to use? It would be helpful to quote the entire problem exactly, rather than refer to a different source.
Sullivan provided the following hint:

Little r = 3960 miles in terms of Earth's radius.

In terms of r and h, I found the following online:

r = radius of Earth in terms of miles.

h = deck height of 100 feet above sea level.

#### Dr.Peterson

##### Elite Member
A similar question (using different numbers) found online provided the following information:

"The mathematically correct formula is d^2 = 2*r*h where d is the distance to the horizon, r is the radius of the earth, and h is the height above sea level, all in the same units."
In order to use the same units, you have to either convert radius to feet, and get the answer in feet, or convert the height to miles, and get the distance in miles. You haven't done that yet.

Sullivan provided the following hint:

Little r = 3960 miles in terms of Earth's radius.

In terms of r and h, I found the following online:

r = radius of Earth in terms of miles.

h = deck height of 100 feet above sea level.
I asked whether Sullivan gave you the same equation, and defined the variables in the same way, as you say you found online. Otherwise, I don't know what you'd be expected to do, since this is essential information for solving the problem. I have to assume he did.

But I doubt that he said exactly as you quote, "3960 miles in terms of Earth's radius", which doesn't sound normal to me. Can you please quote the entire problem from the book, including the formula?

But do you understand the importance of the variable definitions, and the conversion they require? That's the important point here.

#### harpazo

##### Full Member
In order to use the same units, you have to either convert radius to feet, and get the answer in feet, or convert the height to miles, and get the distance in miles. You haven't done that yet.

I asked whether Sullivan gave you the same equation, and defined the variables in the same way, as you say you found online. Otherwise, I don't know what you'd be expected to do, since this is essential information for solving the problem. I have to assume he did.

But I doubt that he said exactly as you quote, "3960 miles in terms of Earth's radius", which doesn't sound normal to me. Can you please quote the entire problem from the book, including the formula?

But do you understand the importance of the variable definitions, and the conversion they require? That's the important point here.
1. Sullivan did not provide the same equation and defined r and h the same way. In fact, I think Sullivan used different variables in his sample question.

2. Sullivan said to use radius of Earth as 3960 miles.

3. I am not home now. The textbook is at home.

4. I do understand the importance of the variable definitions and the conversion they each require to make the problem clear and reasonable.

#### harpazo

##### Full Member
Check your units! Are your r and h given in the same units?

Also, does the answer make sense?

I assume Sullivan gave the same equation to use? It would be helpful to quote the entire problem exactly, rather than refer to a different source.
100 ft = 0.01894 miles
x^2 = 3960.01894^2 - 3960^2
x=12.25 miles

#### Dr.Peterson

##### Elite Member
Interesting ... now you're using a different formula that you've never shown us! Next time, please quote the entire problem as given, including such details. It can make a big difference in how we need to help.

Are you implying that whereas another site gave you the approximate formula d^2 = 2*r*h (but called it "mathematically correct"), Sullivan gave you the exact formula, x^2 = (r + h)^2 - r^2? Do you see that these are not exactly equivalent, but will be very close when h is small relative to r?

But the answer is correct, now. Good work.

#### harpazo

##### Full Member
Interesting ... now you're using a different formula that you've never shown us! Next time, please quote the entire problem as given, including such details. It can make a big difference in how we need to help.

Are you implying that whereas another site gave you the approximate formula d^2 = 2*r*h (but called it "mathematically correct"), Sullivan gave you the exact formula, x^2 = (r + h)^2 - r^2? Do you see that these are not exactly equivalent, but will be very close when h is small relative to r?

But the answer is correct, now. Good work.
Yes, I can see that the formulas are not the same.