Question

1. choose the correct answer.

image of triangle def with sides: de=6 cm, ef=3 cm, df=5 cm
a = 3 cm, b = 5 cm, c = 6 cm
the triangle is a(n) ____ triangle.
options: right, obtuse, acute

Explanation:

Step1: Recall the triangle inequality theorem for types

For a triangle with sides \(a\), \(b\), \(c\) (where \(c\) is the longest side), we use the Pythagorean theorem's extension: \(a^{2}+b^{2}\) vs \(c^{2}\). If \(a^{2}+b^{2}=c^{2}\), right; \(a^{2}+b^{2}c^{2}\), acute.
Here, \(a = 3\), \(b = 5\), \(c = 6\). Calculate \(a^{2}+b^{2}=3^{2}+5^{2}=9 + 25=34\), \(c^{2}=6^{2}=36\).

Step2: Compare the values

Since \(34<36\) (i.e., \(a^{2}+b^{2}eq36\), so \(F\) is not a right angle. Wait, maybe my initial assumption is wrong. Wait, let's recalculate. Wait, \(a = 3\), \(b = 5\), \(c = 6\). Longest side is \(c = 6\). So \(a^{2}+b^{2}=9 + 25 = 34\), \(c^{2}=36\). Since \(34<36\), so the triangle is obtuse? Wait, no, wait, the formula is: if \(c\) is the longest side, then:

• \(a^{2}+b^{2}=c^{2}\): right triangle.
• \(a^{2}+b^{2}>c^{2}\): acute triangle (all angles less than 90°).
• \(a^{2}+b^{2}

Wait, so \(34<36\), so \(a^{2}+b^{2}

Answer:

obtuse (the option with "obtuse" as the text, so the second option: obtuse)