Chapter A.2, Problem 52AYU

To determine

Approximate the actual distance from San Juan to Hamilton and Hamilton to Fort Lauderdale.

Answer to Problem 52AYU

  $\boxed{1028miles}$ , $\boxed{965miles}$

Explanation of Solution

Given information:

Karen is doing research on the Bermuda Triangle, which she defines roghly by Hamilton, Bermuda; San Juan, Puerto Rico; and Fort Lauderdale, Florida.on her atlas Karen measures the straight line distances from Hamilton to Fort Lauderdale, Fort Lauderdale to Sanjuan and San Juan to Hamilton to be approximately $57mm$ , $58mm$ and $53.5mm$ respectively. If the actual from Fort Lauderdale to San Juan is $1046miles$ , approximate the actual distance from San Juan to Hamilton and Hamilton to Fort Lauderdale.

  

Calculation:

Consider the illustration,

Let $x$ be the actual distance between the first place to the second place, and $y$ the actual distance between the third place and the first place.

We know that two triangles are equal if the corresponding angles are equal and the lengths of the corresponding sides are proportional.

Since the corresponding angles of similar triangles are proportional, we get

  $\frac{57}{x}=\frac{58}{1046}=\frac{53.5}{y}$

Now solve for $x$ , multiply both side by $x$ ,

  $\begin{array}{l}x\left(\frac{57}{x}\right)=x\left(\frac{58}{1046}\right)\\ 57=x\left(\frac{29}{523}\right)\\ x=\left(\frac{523}{29}\right)\times 57\\ x=1028\end{array}$

The distance between the first place to the second place is $1028miles$

Now solve for y.

  $\frac{58}{1046}=\frac{53.5}{y}$

  $\begin{array}{l}y\left(\frac{58}{1046}\right)=y\left(\frac{53.5}{y}\right)\\ y\left(\frac{58}{1046}\right)=53.5\\ y=\left(\frac{1046}{58}\right)\times 53.5\\ y=965miles\end{array}$

Hence,the actual distance from San Juan to Hamilton and Hamilton to Fort Lauderdale is $\boxed{1028miles}$ , $\boxed{965miles}$ .