Chapter 53, Problem 1A

Determine the length of a. Round the answer to 1 decimal place.

To determine

The length of side a of the given triangle.

Answer to Problem 1A

The length of side a is $a=28.39\text{mm}$.

Explanation of Solution

Given:

The following figure is given.

  

If one of the angles of any triangle is denoted by a rectangle, the angle is considered as a right angle. In the figure above, the angle B is the right angle and triangle ABC is the right-angle triangle.

To calculate the side BC, let us apply the Pythagoras theorem. According to Pythagoras theorem,

  $\begin{array}{l}A{C}^2=A{B}^2+B{C}^2\\ {\left(63.5\right)}^2={\left(56.8\right)}^2+{\left(a\right)}^2\\ {\left(a\right)}^2={\left(63.5\right)}^2-{\left(56.8\right)}^2\\ {\left(a\right)}^2=806.01\\ a=\sqrt{806.01}\\ a=28.39\text{mm}\end{array}$

The length a of the given triangle is $a=28.39\text{mm}$.