Suppose a triangle has sides [tex]$a, b$[/tex], and [tex]$c$[/tex], and that [tex]$a^2+b^2 < c^2$[/tex]. Let [tex]$\theta$[/tex] be the angle opposite side [tex]$c$[/tex]. Which of the following statements is true?
A. The triangle is not a right triangle.
B. [tex]$\cos \theta<0$[/tex]
C. [tex]$a^2+b^2-c^2=2 a b \cos \theta$[/tex]
D. [tex]$\cos \theta>0[/tex]
Answer (2)
Given the inequality a 2 + b 2 < c 2 , the triangle cannot be a right triangle, meaning A is true. Additionally, this indicates that the angle opposite the longest side c is obtuse, making cos θ < 0 . Therefore, the correct answer is option A.
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A, C and D ;
