Chapter 8, Problem 29RE

Finding the Distance to Shore The Willis Tower in chicago is 1454 feet tall and is situated about 1 mile inland from the shore of Lake Michigan, as indicated in the figure on the top right. An observer in a pleasure boat on the lake directly in front of the Willis Tower looks at the top of the tower and measures the angle of elevation as $5°$. How far offshore is the boat?

To determine

To find: How far off shore is the boat?

Answer to Problem 29RE

The boat is approximately $11,339.30\text{ feet}$ or $2.15\text{ miles}$, from shore.

Explanation of Solution

Given:

The Willis Tower in Chicago is 1454 feet tall and is situated about 1 mile inland from the shore of Lake Michigan, as indicated in the figure on the top right. An observer in a pleasure boat on the lake directly in front of the Willis Tower looks at the top of the tower and measures the angle of elevation as $5°$.

Formula used:

$\text{tanθ }=\text{ opp}/\text{adj}$

Calculation:

Let $x$ be the distance the boat is from the shore.

$1 mi=5280 ft$

$\tan 5°=\frac{1454}{\left(5280+x\right)}$

$5280+x=\frac{1454}{\text{tan}5}$

$x=11,339.30 \text{feet}$

$x=\frac{11,339.30}{5280}\text{ miles }\approx 2.15 \text{miles}$

The boat is approximately $11,339.30\text{ feet}$ or $2.15\text{ miles}$, from shore.