Chapter 4.4, Problem 97E

(a)

To determine

The distance, d from the observer to the plane if an airplane, flying at an altitude of 6 miles, is on a flight path that passes directly over an observer, the angle of elevation from the observer to the planeis $\theta ={30}^0$ .

  

Answer to Problem 97E

The distance, d from the observer to the plane is 12 miles

Explanation of Solution

Given info:

  $\theta ={30}^0$

Opposite side = 6 miles

Formula used:

  $\sin \theta =\frac{\text{Opposite side}}{\text{Hypotenuse}}$

Calculation:

Given that $\theta ={30}^0$ ,

We have

  $\begin{array}{l}\sin \theta =\frac{\text{Opposite side}}{\text{Hypotenuse}}\\ \sin 30=\frac{6}{d}\\ d=\frac{6}{\frac{1}{2}}=12miles\end{array}$

Conclusion:

Thus,the distance, d from the observer to the plane is 12 miles

(b)

To determine

The distance, d from the observer to the plane if an airplane, flying at an altitude of 6 miles, is on a flight path that passes directly over an observer, the angle of elevation from the observer to the plane is $\theta ={90}^0$ .

  

Answer to Problem 97E

The distance, d from the observer to the plane is 6 miles

Explanation of Solution

Given info:

  $\theta ={90}^0$

Opposite side = 6 miles

Formula used:

  $\sin \theta =\frac{\text{Opposite side}}{\text{Hypotenuse}}$

Calculation:

Given that $\theta ={90}^0$ ,

We have

  $\begin{array}{l}\sin \theta =\frac{\text{Opposite side}}{\text{Hypotenuse}}\\ \sin 90=\frac{6}{d}\\ d=\frac{6}{1}=6miles\end{array}$

Conclusion:

Thus,the distance, d from the observer to the plane is 6 miles

(c)

To determine

The distance, d from the observer to the plane if an airplane, flying at an altitude of 6 miles, is on a flight path that passes directly over an observer, the angle of elevation from the observer to the plane is $\theta ={120}^0$ .

  

Answer to Problem 97E

The distance, d from the observer to the plane is 12 miles

Explanation of Solution

Given info:

  $\theta ={120}^0$

Opposite side = 6 miles

Formula used:

  $\sin \theta =\frac{\text{Opposite side}}{\text{Hypotenuse}}$

Calculation:

Given that $\theta ={120}^0$ ,

We have

  $\begin{array}{l}\sin \theta =\frac{\text{Opposite side}}{\text{Hypotenuse}}\\ \sin 120=\frac{6}{d}\\ d=\frac{6}{\frac{1}{2}}=12miles\end{array}$

Conclusion:

Thus,the distance, d from the observer to the plane is 12 miles