Chapter 4.6, Problem 85E

To determine

Graph the function as $d$ over the interval $0<x<\pi$

Answer to Problem 85E

  

Explanation of Solution

Given information:

A plane flying at an altitude of 7 miles above a radar antenna will pass directly over the radar antenna (see figure). Let $d$ be the ground distance from the antenna to the point directly under the plane and let $x$ be the angle of elevation to the plane from the antenna.(d is positive as the plane approaches the antenna.)Write $d$ as a function of and graph the function over the interval $0<x<\pi$ .

Calculation:

Let us consider the points to write $d$ as a function of angle .

Let $A$ be the point where camera is situated.

  $B$ is the point on the street where the parade will be passing left to right.

  $C$ is the point where particular unit of parade will reach.

So here, the points form a right angled triangle(right angled at $B$ )

In triangle $ABC$ ,

Ground distance of the plane from the antenna= $d$

Altitude of the flying plane= $7$ miles

Angle of elevation to the plane from antenna = $x$

Now using,

  $\tan x=\begin{array}{c}AB\\ BC\end{array}$

  $\tan x=\begin{array}{c}7\\ d\end{array}$

  $d=\begin{array}{c}7\\ \tan x\end{array}$

Now, let us plot $d=\begin{array}{c}7\\ \tan x\end{array}$ over the interval $0<x<\pi$ ,

  

Hence the above graph represents the $d$ as a function of $x$ over the interval $0<x<\pi$ .