Chapter 15.2, Problem 10PSB

(a)

To determine

To Find: The longest segment in the given figure.

Answer to Problem 10PSB

  $DA\text{ is the longest segment}\text{.}$

Explanation of Solution

Given:

  

Formula Used:

Angle-Sum theorem: Sum of interior angle of a triangle is 180.

Calculation:

  $\begin{array}{l}\angle CAB=180-90-30\\ \angle CAB={60}^0\\ \angle CDA=180-80-55\\ \angle CDA={45}^0\\ \angle CAB>\angle CDA\\ DA\text{ is the longest segment}\text{.}\end{array}$

Conclusion:

Thus, $DA\text{ is the longest segment}\text{.}$

(b)

To determine

To Find: The shortest segment in the given figure.

Answer to Problem 10PSB

  $\text{ZY is the smallest segment}$

Explanation of Solution

Given:

  

Formula Used:

Angle-Sum theorem: Sum of interior angle of a triangle is 180.

Calculation:

  $\begin{array}{l}\angle ZXY=180-90-30\\ \angle ZXY={60}^0\\ \angle ZXW=30+90\\ \angle ZXW={120}^0\\ \angle ZWX=180-120-30\\ \angle ZWX={30}^0\\ \text{since }\angle ZWX\text{ is the smallest angle }\left(\text{opposite side of the smallest angle is the smallest segment}\text{.}\right)\\ \text{ZY is the smallest segment}\end{array}$

Conclusion:

Thus, $\text{ZY is the smallest segment}$