Question

Determine if the segment lengths form a triangle. If so, would the triangle be acute, right, or obtuse? 4.1, 8.2, 12.2

Answer 1

Three line segments can form a triangle if the length of the longest segment is greater than the sum of the lengths of the shorter segments.

 $4.1 + 8.2 \ \textgreater \ 12.2 \\ 12.3 \ \textgreater \ 12.2 \\ true$
They can form a triangle.

Now 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 $c^2\ \textless \ a^2+b^2$, the triangle is acute
- if $c^2\ \textgreater \ a^2+b^2$, the triangle is obtuse

$4.1^2+8.2^2=16.81+67.24=84.05 \\ 12.2^2=148.84 \\ \\ 148.84\ \textgreater \ 84.05$
The triangle is obtuse.

The answer is D.