Chapter 10, Problem 5CRP

Explanation of Solution

The length of the image of the pole in the projection plane is:

The height of the pole is eight foot, the distance between the one end of the pole and the center of projection is four feet.

The given condition is shown in the figure below:

Explanation:

From the above figure, it is clear that the length of the image is the length between the points ${\text{P}}_{\text{r}}$ and ${\text{P}}_{\text{r}}{}^{\prime }$.

In the given case the pole is parallel to the projection plane. So, from the properties of the similar triangle if all the three angle of any two triangle is same both the triangles are similar triangle, that is the triangle $\text{P}-\text{C}-{\text{P}}^{\prime }$ and triangle ${\text{P}}_{\text{r}}-\text{C}-{\text{P}}_{\text{r}}{}^{\prime }$ are similar.

From the properties of the similar triangle the corresponding sides are all in the same ratio.

$\frac{{\text{P}}_{\text{r}}\text{C}}{\text{PC}}=\frac{{\text{P}}_{\text{r}}{\text{P}}_{\text{r}}{}^{\prime }}{\text{P}{\text{P}}^{\prime }}$

Substitute $8$