Chapter 8.3, Problem 7WE

i.

To determine

Whether the given sides are the sides of acute, right or obtuse angle triangle.

Answer to Problem 7WE

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

Explanation of Solution

Given information:

The sides of a triangle are 0.5, 1.2, 1.3

Let ABC be a triangle.

Also let a=0.5, b=1.2 and c=1.3 then

  $\begin{array}{l}{c}^2=a^2+b^2\\ $ {(1.3)}^2={(0.5)}^2+{(1.2)}^2$1.69=0.25+1.44\\ 1.69=1.69\end{array}$

Therefore from the converse of Pythagoras theorem $\angle C=90°$

So, the given sides of the triangles are the sides of right angle triangle.

ii.

To determine

Whether the given sides are the sides of acute, right or obtuse angle triangle.

Answer to Problem 7WE

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

Explanation of Solution

Given information:

The sides of a triangle are 5n, 12n, 13n where n>0

Let ABC be a triangle.

Also let a=5n, b=12n and c=13n

We see that

  $\begin{array}{l}{c}^2=a^2+b^2\\ $ {(13n)}^2={(5n)}^2+{(12n)}^2$169n^2=25n^2+144n^2\\ 169n^2=169n^2\end{array}$

Therefore from the converse of Pythagoras theorem $\angle C=90°$

So, the given sides of the triangles are the sides of right angle triangle.