Chapter 8, Problem 27CT

To determine

To find: The distance between the boat and the base of the light house.

Answer to Problem 27CT

The distance between the boat and the base of the light house is 257 m.

Explanation of Solution

Given:

The angle of depression is $4°$ . Height of the light house is 18 m.

Calculation:

Diagram for the given condition is shown below:

  

Take tan of given angle of depression of above right triangle as follows:

  $\begin{array}{l}\tan 4°=\frac{AB}{BC}\\ 0.07=\frac{18}{BC}\\ BC\approx 257\text{m}\end{array}$

Thus, the distance between the boat and the base of the light house is 257 m.