Chapter 15.2, Problem 7PSB

To determine

To Find: The side opposite to the given angle.

Answer to Problem 7PSB

Middle Side

Explanation of Solution

Given:

  ${\text{Scalene triangle with one angle as 60}}^0$

Formula Used:

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

Calculation:

  $\begin{array}{l}{\text{one angle of scalene triangle is 60}}^0\\ \text{consider the second angle = 60+}x\\ \text{so the third angle is = }60-x\\ {\text{and it satisfies the condition that all the angles sum upto 180}}^0\\ \text{where }x\text{ is positive real number}\text{.}\\ \text{Now we have the largest angle as }60+x\\ \text{and the smallest angle as }60-x\\ {\text{ so being the middle angle the side opposite to 60}}^0\text{ is the middle side}\text{. }\end{array}$

Conclusion:

Thus the side opposite to the given angle is middle side.