Chapter 15, Problem 31CR

To determine

To Find: Thegiven triangle is acute, obtuse or right angled.

Answer to Problem 31CR

  $\Delta ARO\text{ is an acute angled triangle}$

Explanation of Solution

Given:

  

Formula Used:

  $\begin{array}{l}\text{ for acute }\Delta \\ a^2+b^2>c^2\end{array}$

  $\begin{array}{l}\text{for obtuse triangle}\\ a^2+b^2<c^2\end{array}$

  $\begin{array}{l}\text{For right angle triangles}\\ {\text{a}}^2+b^2=c^2\end{array}$

Calculation:

  $\begin{array}{l}let\\ a=AR=8\\ b=RO=13\\ c=AO=15\\ A{R}^2=64\\ O{R}^2=169\\ A{O}^2=225\\ \text{⇒}{8}^2+{13}^2>{15}^2\\ \text{⇒}233>225\\ \Delta ARO\text{ is acute angled triangle}\text{.}\end{array}$

Conclusion:

Thus, $\Delta ARO\text{ is acute angled triangle}$ .