Chapter 8.3, Problem 3WE

To determine

To state: state whether the given sides are the sides of acute angle triangle, right angles or obtuse angle.

Answer to Problem 3WE

The given sides of triangle are the sides of right angle triangle.

Explanation of Solution

Given information: We have the given the sides of triangle are $8,8\sqrt{3},16$

Let ABC be a triangle.

Also let $a=8,b=8\sqrt{3}andc=16$

We see that

  $\begin{array}{c}{c}^2=a^2+b^2\\ {\left(16\right)}^2={\left(8\right)}^2+{\left(8\sqrt{3}\right)}^2\\ 256=64+192\\ 256=256\end{array}$

Therefore from the converse of Pythagoras theorem if $c^2=a^2+b^2$ then $\Delta ABC$ is right triangle.