Chapter 15.2, Problem 3PSA

(a)

To determine

To Find: The shortest and longest side of the triangle.

Answer to Problem 3PSA

PQ is the longest

PR is the shortest

Explanation of Solution

Given:

  $\Delta PQR$

  $\begin{array}{l}\angle P={67}^0\\ \angle Q={23}^0\end{array}$

Formula Used:

Angle Sum Theorem: Sum of interior angle is equal to 180.

Calculation:

  $\begin{array}{l}\text{As per the angle sum theorem}\\ x+67+23=180\\ x=180-90\\ x=90\end{array}$

  $\begin{array}{l}\text{Longest side = PQ }\left(\text{opposite side of the largest angle}\right)\\ \text{Shortest side = PR }\left(\text{opposite side of the smallest angle}\right)\end{array}$

Conclusion:

Thus, PQ is the longest and PR is the shortest side in the given triangle

(b)

To determine

To Find:The name given to the required side.

Answer to Problem 3PSA

  $\overrightarrow{PQ}\text{}\text{ is called the Hypotenuse}\text{.}$

Explanation of Solution

Given:

  $\angle PRQ={90}^0$

Formula Used:

Angle Sum Theorem: Sum of interior angle is equal to 180.

Calculation:

Side opposite to the right angle in right-angles triangle is hypotenuse.

  $\begin{array}{l}\text{Since }\angle PRQ={90}^0\\ \overrightarrow{PQ}\text{}\text{ is the Hypotenuse}\text{.}\end{array}$

Conclusion:

Thus, $\overrightarrow{PQ}\text{}\text{ is the Hypotenuse}\text{.}$