Question

determine which sets of lengths can form a right triangle.

Explanation:

Step1: Check the first set (30, 60, 90)

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side.
\(30^{2}+60^{2}=900 + 3600=4500\), \(90^{2}=8100\). Since \(4500
eq8100\).

Step2: Check the second set (10, 24, 26)

\(10^{2}+24^{2}=100 + 576 = 676\), \(26^{2}=676\). Since \(10^{2}+24^{2}=26^{2}\).

Step3: Check the third set (6, 14, 18)

\(6^{2}+14^{2}=36+196 = 232\), \(18^{2}=324\). Since \(232
eq324\).

Answer:

For \(30,60,90\): No.
For \(10,24,26\): Yes.
For \(6,14,18\): No.