Chapter 10.8, Problem 2CE

To determine

To analyze: the diagram and to explain the solution.

Explanation of Solution

Given:

  $\Delta ABC$ with $m\angle C=90°$ ; $AC=r;AB=s$ :

  

The given part,

  $\Delta ABC$ with $m\angle C=90°$ , $AC=r;AB=s$ :

  

Now, consider the first solution,

  $m\angle C=90°$ ; $AC=r;AB=s$ .

  

Now, draw a line segment $AB=s$ , and draw a semi-circle as shown below:

  

Now, measure $r$ cutting at a point on the semi circle:

  

Join the point and name it as $AC=r$ , and join all other points:

  

Thus, the final figure is shown below:

  

Now, consider the second solution,

  

Now, again considering first solution,

  $m\angle C=90°$ , $AC=r\text{ and }AB=s$

  

Drawing a line segment on which there is a point $C$ and drawing a perpendicular line from $C$ forming a line segment of $AC=r$ as shown below:

  

Now, measuring a line segment from $A$ to the line through which $C$ passes with the measure of $s$ .

  

Joining the point and naming it as $AB=s$ and joining all the other points,

  

Thus, the final figure is shown below:

  

Conclusion:

Both the solutions and both the approaches of solving them are correct.