Chapter 8.3, Problem 8WE

a.

To determine

To write: Whether the triangle with sides of the given lengths is acute, right or obtuse.

Answer to Problem 8WE

Right triangle

Explanation of Solution

Given information: Sides of a triangle are equal to $33,44,55$

Let $a,b,c$ be the sides of triangle

If $a^2+b^2=c^2$ , then the given triangle will be a right triangle.

Take $a=33,b=44,c=55$

  $\begin{array}{l}{a}^2+b^2={33}^2+{44}^2=1089+1936=3025\\ c^2={55}^2=3025\end{array}$

So,

  $a^2+b^2=c^2$

Therefore,

The triangle is a right triangle.

b.

To determine

To write: Whether the triangle with sides of the given lengths is acute, right or obtuse.

Answer to Problem 8WE

Right triangle

Explanation of Solution

Given information: Sides of a triangle are equal to $3n,4n,5n$

Let $a,b,c$ be the sides of triangle

If $a^2+b^2=c^2$ , then it is a right triangle.

Take $a=3n,b=4n,c=5n$

  $\begin{array}{l}{a}^2+b^2={\left(3n\right)}^2+{\left(4n\right)}^2=9n^2+16n^2=25n^2\\ c^2={\left(5n\right)}^2=25n^2\end{array}$

So,

  $a^2+b^2=c^2$

Therefore,

The triangle is a right triangle.