Chapter 4, Problem 143CR

To determine

To Compute : The distance between two towns visible by the passenger travelling in the airplane.

Answer to Problem 143CR

The distance between the two towns is $952.44fts$.

Explanation of Solution

Given information :

  

AB is 37,000 fts , considering A as the passenger in the airplane above the ground. And let D and C be the two towns x and x + y feet far from B respectively. The angle of depression from the airplane to D and C towns are $32°$ and $76°$ respectively.

According to informations given,

  $\tan 32°=\frac{x}{37,000}$

That is,

  $x=\tan 32°\times 37,000$

And,

  $\tan 76°=\frac{x+y}{37,000}$

That is,

  $x+y=37,000\times \tan 76°$

Therefore,

The distance between the two towns D and C, that is y is obtained by,

  $y=BC-BD$

  $y=37,000\times \tan 76°-\tan 32°\times 37,000$

  $y=37,00(\tan 76°-\tan 32°)$

y = $952.44fts$

Thus,

The distance between two towns is approximately $952.44fts$ .