Question

The lengths of the sides of a triangle are given. Classify each triangle as acute, right, or obtuse.A. 4, 5, 6B. 11, 12, 15

Answer 1

To find out if a triangle is acute, right or obtuse we need to use the following rules:

$\begin{gathered} a^2+b^2>c^2\Rightarrow acute \\ a^2+b^2=c^2\Rightarrow right\text{ } \\ a^2+b^2where c is the largest side of the triangle and a and b are the other two sides.

A.

In this case c=6 and we can take the other two as a=4, b=5. Then:

[tex]\begin{gathered} 4^2+5^2?6^2 \\ 16+25\text{?}36 \\ 41>36 \end{gathered}$

Therefore triangle A is an acute triangle.

B.

In this case c=15, b=12 and a=11. Then:

$\begin{gathered} 11^2+12^2?15^2 \\ 121+144\text{?}225 \\ 265>225 \end{gathered}$

Therefore triangle B is an acute triangle.