Question

which sets of three of numbers represent the sides of an obtuse triangle? check all that apply. 4,7,8 3,4,5 2,2,3 6,8,9 3,5,6

Explanation:

Step1: Recall obtuse triangle rule

For sides $a \leq b \leq c$, triangle is obtuse if $a^2 + b^2 < c^2$, and valid if $a + b > c$.

Step2: Test set 4,7,8

$4^2 + 7^2 = 16 + 49 = 65$, $8^2 = 64$. $65 > 64$ → Acute.

Step3: Test set 3,4,5

$3^2 + 4^2 = 9 + 16 = 25$, $5^2 = 25$. $25 = 25$ → Right.

Step4: Test set 2,2,3

$2^2 + 2^2 = 4 + 4 = 8$, $3^2 = 9$. $8 < 9$ → Obtuse.

Step5: Test set 6,8,9

$6^2 + 8^2 = 36 + 64 = 100$, $9^2 = 81$. $100 > 81$ → Acute.

Step6: Test set 3,5,6

$3^2 + 5^2 = 9 + 25 = 34$, $6^2 = 36$. $34 < 36$ → Obtuse.

Answer:

2, 2, 3
3, 5, 6