Question

Suppose a triangle has sides a, b, and c, and the angle opposite the side of length b is obtuse. What must be true?

A. a^2 + c^2 < b^2
B. a^2 + c^2 > b^2
C. b^2 + c^2 < a^2
D. a^2 + b^2 < c^2

Answer 1

Draw it out. If it's an obtuse angle, it's larger than 90 degrees and the side opposite the angle is huge because you need to connect the alligator jaws. Lol

This pic sucks in that the letters don't match up properly. But the square of the smaller sides will ALWAYS be less than the square of the opposite side for an obtuse triangle. You should test this yourself.

Answer 2

a^2+b^2=c^2 is a right angled triangle.

You're given that a^2+b^2>c^2
cos(A) = [a^2+b^2-c^2]/2ab
c^2+2ab*cos(A) = a^2+b^2
Thus, c^2+2ab*cos(A) > c^2
cos(A)>0
A>90 degrees. ie Obtuse triangle.

If a^2+b^2 < c^2.
A<90 degrees ie. Acute triangle.
Hypotenuse is c.

Use the law of cosines.