Question

a triangle. 11, 15, 16, 21 12 not a △ acute right obtuse

Explanation:

Step1: Check triangle inequality

For three side lengths \(a,b,c\) (\(c\) is the longest side), \(a + b>c\). Here \(a = 11\), \(b = 15\), \(c = 21\). \(11+15=26>21\), \(11 + 16=27>21\), \(15+16 = 31>21\). So it is a triangle.

Step2: Use the Pythagorean theorem extension

For a triangle with side lengths \(a,b,c\) (\(c\) is the longest side), if \(a^{2}+b^{2}>c^{2}\), it is acute; if \(a^{2}+b^{2}=c^{2}\), it is right; if \(a^{2}+b^{2}\(a = 11\), \(b = 16\), \(c = 21\). \(a^{2}+b^{2}=11^{2}+16^{2}=121 + 256=377\), \(c^{2}=21^{2}=441\). Since \(377<441\) (i.e., \(a^{2}+b^{2}

Answer:

Obtuse