Chapter 11.2, Problem 40E

To determine

To find: thedistance of the boat from the base of the cliff.

Answer to Problem 40E

  $521.02\text{ feet}$ .

Explanation of Solution

Given:

The height of the cliff is $200-\text{foot}$

The angle of depression of the boat from the top of the cliff is ${21}^{\circ }$ .

Calculation:

According to the question,

Let x be the distance between boat and cliff.

Now, make a diagram to represent the situation:

conclude the value of x using the trigonometric relationships.

  $\begin{array}{l}\tan {21}^{\circ }=\frac{200}{x}\\ \therefore x=\frac{200}{\tan {21}^{\circ }}\\ \Rightarrow x\approx 521.02\text{ feet}\end{array}$

Hence, the distance of the boat from the base of the cliff is $521.02\text{ feet}$ .