Chapter 9.3, Problem 43E

To determine

To find: how far to the east and north of the origin is that point.

Answer to Problem 43E

The east distance is $75m$ and the north distance is $118.30m$ .

Explanation of Solution

Given information: A sod farm can use a combined Cartesian and polar coordinate system to identify points in the field. Points have coordinates of the form $\left(x,y,r,\theta \right)$ . The sprinkler heads are spaced $25m$ apart. The polar coordinates give the location of the point relative to the sprinkler head. If a point has coordinates $\left(4,3,2,{120}^{\circ }\right)$ .

Calculation:

The horizontal distance:

  $\begin{array}{l}25\left(x+r\cos \theta \right)\\ \Rightarrow 25\left(4+2\cos 120\right)\\ \Rightarrow 75m\left(east\right)\end{array}$

The vertical distance:

  $\begin{array}{l}25\left(x+r\sin \theta \right)\\ \Rightarrow 25\left(3+2\sin 120\right)\\ \Rightarrow 118.30m\left(north\right)\end{array}$