Answer:
A.\(Cos\theta<0\)
B.The triangle is not a right triangle
C.\(\theta\) is an obtuse angle
Step-by-step explanation:
We are given that a triangle with sides a, b and c.
\(a^2+b^2
When a triangle is an obtuse triangle then
\(a^2+b^2
It means given triangle is an obtuse triangle .
Obtuse triangle is that triangle in which one angle is an obtuse angle.
Let \(\theta\) be the measure of angle opposite the side of length c.
We have to find the statements which are must be true.
Cosine law:
\(c^2=a^2+b^2-2abCos\theta\)
Substitute the value then we get
\(c^2
Subtracting \(c^2\) on both sides of inequality
\(c^2-c^2
\(0<-2ab Cos\theta\)
Adding \(2abCos\theta\) on both sides then we get
\(2abCos\theta<-2abCos\theta+2abCos\theta=0\)
\(2abCos\theta<0\)
\(Cos\theta<0\)
\(Cos\theta\)is negative in second quadrant and third quadrant.
Therefore, \(\frac{\pi}{2}<\theta<\frac{3\pi}{2}\)
But, we know that an obtuse angle is that angle which is greater than 90 degrees and less than 180 degrees.
Hence, \(\frac{\pi}{2}<\theta<\pi\)
Option A ,C and D are true.
