Chapter 12.7, Problem 8P

To determine

To determinethat how far is the hang glider from the nearer end of the field.

Answer to Problem 8P

The distance to the nearest end of the field that is 16849.

Explanation of Solution

Given information :

Anles of dipression of field are given as ${24}^{\circ }$ and ${30}^{\circ }$

  

Here $\angle BAD=6^{\circ }$

We have to find AD.

Now according to law of sines,

In any triangle ABC,

  

  $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

Hence,

  $\begin{array}{l}\frac{5000}{\sin 6^{\circ }}=\frac{AD}{\sin {24}^{\circ }}\\ AD=\frac{\sin {24}^{\circ }\times 5000}{\sin 6^{\circ }}\\ AD=19456\end{array}$

Hence AD is 19456 ft.

Now we have to find the distance to the nearest end of the field that is DC.

We know,

  $\begin{array}{l}\cos {30}^{\circ }=\frac{DC}{AD}\\ DC=16849\end{array}$

Hence distance is 16849 ft.