Chapter A.2, Problem 52AYU

To determine

To find: The approximate the actual distances from San Juan to Hamilton and from Hamilton to Fort Lauderdale.

Answer to Problem 52AYU

$964.85$ and $1027.97$.

Explanation of Solution

Given:

Karen is doing research on the Bermuda Triangle, which she defines roughly 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 San Juan, and San Juan to Hamilton to be approximately 57 millimeters (mm), 58 mm, and $53.5$ mm respectively. If the actual distance from Fort Lauderdale to San Juan is 1046 miles.

Calculation:

By the similar triangle theorem, which states that a triangle with the same angles has proportionate sides.

The actual distance from Fort Lauderdale to San Juan is 1046 miles, but approximate distance in atlas is 58 mm. Therefore the ratio is $\frac{1046}{58}=\frac{523}{29}$.

The approximate the actual distances from San Juan to Hamilton $=53.5\times \frac{523}{29}=964.85$.

The approximate the actual distances from Hamilton to Fort Lauderdale$=57\times \frac{523}{29}=1027.97$.