Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

How Far Is the Ship From Shore?

A person who is 6 feet tall is standing on the beach in Fort Lauderdale, Florida, and looks out onto the Atlantic Ocean. Suddenly, a ship appears on the horizon. How far is the ship from shore?

Given Data:

Radius of Earth = 3960 miles.

One mile = 5280 feet.

Looking for the set up equation. I can take it from there.

Also, can right triangle trigonometry be used to answer this question? If so, can I have the trigonometric set up equation as well?

Thanks.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: How Far Is the Ship From Shore?

The diagram I posted for a previous lighthouse question will also work here. 

L is the height of the man's eyes.  B is for his feet. O is the centre of the Earth.  H is the ship. Angle LHO is 90.

LO^2 = HO^2 + LH^2  so Pythag rather than sines and cosines.  As trigonmetry means the measurement of triangles Pythag
is also trig.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: How Far Is the Ship From Shore?

The diagram I posted for a previous lighthouse question will also work here. 

L is the height of the man's eyes.  B is for his feet. O is the centre of the Earth.  H is the ship. Angle LHO is 90.

LO^2 = HO^2 + LH^2  so Pythag rather than sines and cosines.  As trigonmetry means the measurement of triangles Pythag
is also trig.

Bob

Yes, I recall the picture. I will play with this question some more.