Chapter A.2, Problem 55AYU

To determine

To find: How far can a person see from the deck? How far can a person see from the bridge, which is 150 feet above sea level? [use the facts that the radius of Earth is 3960 miles and $\text{1 mile }=5280$ feet].

Answer to Problem 55AYU

$12.25$ miles, 15 miles.

Explanation of Solution

Given:

The deck of a destroyer is 100 feet above sea level.

Calculation:

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

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

$\text{100 feet }=\frac{100}{5280}$ miles $=\frac{5}{264}$ miles.

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

${\left(3960+\frac{5}{264}\right)}^2=a^2+{3960}^2$

$15681750=a^2+15681600$

$a^2=150$

$a=12.25$

$12.25$ miles far can a person see from the bridge.

$\text{150 feet }=\frac{150}{5280}$ miles $=\frac{15}{528}$ miles.

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

${\left(3960+\frac{15}{528}\right)}^2=a^2+{3960}^2$

$15681825=a^2+15681600$

$a^2=225$

$a=15$

15 miles far can a person see from the bridge.