Question

given each of the following segment lengths, if they form a triangle, would the triang acute, right, or obtuse?
a) 7, 3, 8

• acute
• right
• obtuse
• the segments do not form a triangle

Explanation:

Step1: Check triangle validity

Verify sum of two sides > third:
$7+3>8$ ($10>8$, true), $7+8>3$ ($15>3$, true), $3+8>7$ ($11>7$, true). Valid triangle.

Step2: Label sides, use triangle inequality

Let $c=8$ (longest), $a=7$, $b=3$. Compare $a^2+b^2$ vs $c^2$:
$a^2+b^2 = 7^2+3^2 = 49+9=58$
$c^2=8^2=64$

Step3: Classify triangle type

Since $a^2+b^2 < c^2$, triangle is obtuse.

Answer:

obtuse