Question

Classify the triangle by its angles based on the side lengths 4.2, 6.4, and 7.6

Answer 1

If c is the length of the longest side and a and b are the lengths of the shorter sides, then:
- if
`c^2=a^2+b^2`, the triangle is right
- if
`c^2<a^2+b^2`, the triangle is acute
- if
`c^2>a^2+b^2`, the triangle is obtuse


`4.2, 6.4, 7.6 \\ \\ a^2+b^2=4.2^2+6.4^2=17.64+40.96=58.6 \\ c^2=7.6^2=57.76 \\ \\ 57.76 \ \textless \ 58.6 \\ c^2 \ \textless \ a^2+b^2`

The triangle is an acute triangle.