Gibb's Hill Lighthouse

[nycmathguy]

College Algebra
Chapter 1/Section 3

Can you work this one out for me?

 

[MathLover1]

here is sketch for you to try do it yourself

to verify the accuracy of these statements use the facts you know about the Pythagorean Theorem, that the radius of Earth is 3960 miles, and 1 mile = 5280 ft

 

[nycmathguy]

here is sketch for you to try do it yourself
View attachment 3868

to verify the accuracy of these statements use the facts you know about the Pythagorean Theorem, that the radius of Earth is 3960 miles, and 1 mile = 5280 ft

Thanks. I will tackle this myself some other day. Brain dead.

 

[nycmathguy]

here is sketch for you to try do it yourself
View attachment 3868

to verify the accuracy of these statements use the facts you know about the Pythagorean Theorem, that the radius of Earth is 3960 miles, and 1 mile = 5280 ft

I can't figure it out even with the information and pictures given. Can you set up the equations needed for me to answer the question? What is the question asking for Exactly? I noticed that you left several numbers given in the application out of your diagram. Just set up the equation(s) needed for me to correctly answer the question.

Thanks

 

[MathLover1]

Using the Pythagorean theorem the first statement was verified using 3960
miles as the earth's radius:

d^2+3960^2=(3960+(362/5280))^2
d^2=(3960+(362/5280))^2-(3960)^2
d=23.3
So the lighthouse cannot be seen from a distance of 26 miles.

The brochure further states that ships 40 miles away can see the light and planes flying at 10,000 feet can See it 120 miles away. Verify the accuracy of these statements. What Assumption did the brochure make about the height of the ship? (Use 3960 as the radius of the earth).

hypothenuse=10,000 feet +3960 miles=3962 miles
first find s
3960+s/5280=sqrt(15683200)
s/5280=3960.202 -3960
s/5280=0.202
s=0.202miles

then
120^2 +(3960+s/5280)^2=3962^2
120^2 +(3960+0.202)^2=3962^2
15697600=15697444 -> approximately same, so result is confirmed

 

[nycmathguy]

Using the Pythagorean theorem the first statement was verified using 3960
miles as the earth's radius:

d^2+3960^2=(3960+(362/5280))^2
d^2=(3960+(362/5280))^2-(3960)^2
d=23.3
So the lighthouse cannot be seen from a distance of 26 miles.

The brochure further states that ships 40 miles away can see the light and planes flying at 10,000 feet can See it 120 miles away. Verify the accuracy of these statements. What Assumption did the brochure make about the height of the ship? (Use 3960 as the radius of the earth).

hypothenuse=10,000 feet +3960 miles=3962 miles
first find s
3960+s/5280=sqrt(15683200)
s/5280=3960.202 -3960
s/5280=0.202
s=0.202miles

then
120^2 +(3960+s/5280)^2=3962^2
120^2 +(3960+0.202)^2=3962^2
15697600=15697444 -> approximately same, so result is confirmed

Mira,

I wanted to tackle the problem on.my own. I requested the set up. The set up often helps me figure out what you did to find the correct equation(s). Thanks for answering the question. If I request the set up, just give me that. If the problem is way above my head, I will say so.