Chapter 15.2, Problem 5PSA

(a)

To determine

To Find: The longest segment in the given figure.

Answer to Problem 5PSA

AB

Explanation of Solution

Given:

  

Formula Used:

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

Calculation:

  $\begin{array}{l}\angle A+\angle B+\angle C=180\\ 50+60+\angle C=180\\ \angle C=180-110\\ \angle C={70}^0\\ \text{since }\angle \text{C is the largest angle, AB is the largest segment}\text{. }\end{array}$

Conclusion:

Thus side AB is the longest segment in the given figure.

(b)

To determine

To Find: The longest segment in the given figure.

Answer to Problem 5PSA

WZ

Explanation of Solution

Given:

  

Formula Used:

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

Calculation:

  $\begin{array}{l}\text{In }\Delta \text{WXZ }\\ \angle {\text{WXZ = 100}}^0\\ \text{In }\Delta \text{XYZ}\\ \angle \text{X}YZ={80}^0\\ \angle X>\angle Y\\ \text{WZ is the longest segment}\text{.}\left(\text{opposite side of the largest angle}\right)\end{array}$

Conclusion:

Thus WZ is the longest segment in the given figure.