Chapter A.2, Problem 54AYU

To determine

To find: How far is the ship from shore?

Answer to Problem 54AYU

3 miles.

Explanation of Solution

Given:

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? [use the facts that the radius of Earth is 3960 miles and 1 mile $=5280$ feet].

Calculation:

$1\text{ miles }=5280\text{ feet}$.

$1\text{ foot }= \frac{1}{5280}\text{ miles}$.

$6\text{ feet }= \frac{6}{5280}\text{ miles = }\frac{1}{880} \text{miles}$.

By Pythagorean Theorem $c^2=a^2+b^2$.

${\left(3960+\frac{1}{880}\right)}^2=a^2+{3960}^2$

$15681609=a^2+15681600$

$a^2=9$

$a=3$

The ship from shore 3 miles apart.