Chapter 71, Problem 1AR

With reference ∠1, name the sides of each of the following triangles as opposite, adjacent, or hypotenuse.

To determine

The name of sides with reference to $\angle 1$.

Answer to Problem 1AR

The names of the sides are

  $\begin{array}{l}\text{Side a = opposite to }\angle \text{1, hence opposite side}\text{.}\\ \text{side b = Adjacent to }\angle \text{1, hence adjacent side}\text{.}\\ \text{side c = Opposite to }right-angleB\text{, hence hypotenuse}\text{.}\end{array}$

Explanation of Solution

Given information:

The given figure is

  

  

Calculation:

In the given triangle, the angle B is the right-angle. Thus, the triangle ABC is a right-angle triangle.

The sides of the triangle are named as follows

  $\begin{array}{l}\text{Side a = opposite to }\angle \text{1, hence opposite side}\text{.}\\ \text{side b = Adjacent to }\angle \text{1, hence adjacent side}\text{.}\\ \text{side c = Opposite to }right-angleB\text{, hence hypotenuse}\text{.}\end{array}$

Conclusion:

Thus, the names of the sides are

  $\begin{array}{l}\text{Side a = opposite to }\angle \text{1, hence opposite side}\text{.}\\ \text{side b = Adjacent to }\angle \text{1, hence adjacent side}\text{.}\\ \text{side c = Opposite to }right-angleB\text{, hence hypotenuse}\text{.}\end{array}$