Question

which of the following must be true?
check ALL that apply,

Answer 1

B and D are true.

_____
The Law of Cosines tells you
.. c^2 = a^2 +b^2 -2ab*cos(θ)
Your problem statement provides a relation involving c^2, so we can substitute to get
.. a^2 +b^2 > a^2 +b^2 -2ab*cos(θ)
.. 0 > -2ab*cos(θ)
.. cos(θ) > 0
In the range 0 ≤ θ ≤ 180°, cos(θ) will be positive for θ < 90°, an acute angle.
Thus A and C are false, B and D are true.