Chapter 9.10, Problem 16PSC

To determine

To find:The distance between the ships to the nearest dm

Answer to Problem 16PSC

The distance between the ships is $668\text{ dm}$

Explanation of Solution

Given information:The following information has been given

Height of the observer is $1000\text{ dm}$

The angles of depression of the ships are ${47}^0$ and ${32}^0$

Formula used:Basic tangent definition has been used

Calculation:We assume that the ships are at a distance of x and y from the vertical line of the observer. Hence, now we find the values of x and y as

  $\tan {32}^0=\frac{1000\text{ dm}}{x}$ and

  $\tan {47}^0=\frac{1000\text{ dm}}{y}$

Thus, now we calculate the values of x and y , and

  $x=1600.35\text{ dm}$ and

  $y=932.488\text{ dm}$

So, the final answer we want is

  $x-y=(1600.35-932.488)\text{ dm}=667.86\text{ dm}$