Chapter 4.6, Problem 86E

To determine

Find d as the function of f and sketch the graph on given condition.

Answer to Problem 86E

  $d=\frac{7}{\tan x}$

Explanation of Solution

Given:

Let A be the point where the plane is directly above the ground.

B is the point on the ground such that the plane is perpendicular to the ground.

C is the point where the radar antenna is situated.

So here, the points A, B and C 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 the antenna= $x$

Let consider the points to write d as function of x

Now, using $\tan x=\frac{\text{perpendicular}}{\text{base}}$

  $\begin{array}{l}\tan x=\frac{AB}{BC}\hfill \\ \tan x=\frac{7}{d}\hfill \\ d=\frac{7}{\tan x}\hfill \end{array}$

Now, plot $d=\frac{7}{\tan x}$ over the interval $0<x<\pi$

  

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