VectorMethod LawOfSines LawOfCosines PlaneGeometry Intermediate

Problem - 2991
Let $\triangle{ABC}$ be an acute triangle and $a, b, c$ be the three sides opposite to $\angle{A}, \angle{B}, \angle{C}$ respectively. If vectors $m=(a+c,b)$ and $n=(a-c, b-a)$ satisfy $m\cdot n = 0$, (1) Compute the measurement of $\angle{C}$. (2) Find the range of $\sin{A} + \sin{B}$.

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