Property 8
(Cosinus Theorem)
\(\cos30^\circ=\frac{\sqrt{3}}{2}\)
\(\cos60^\circ=\frac{1}{2}\)
\(\cos45^\circ=\frac{\sqrt{2}}{2}\)
\(a^2=b^2+c^2-2bc\cdot\cos\alpha\)
1.
\(m\left(\widehat{B}\right)<60^\circ\)
\(\Rightarrow ?<x<?\)
2.
\(x\in\mathbb{Z}\)
\(m\left(\widehat{C}\right)>45^\circ\)
\(\Rightarrow\min\left(x\right)=?\)
3.
\(x\in\mathbb{Z}\)
\(m\left(\widehat{B}\right)>30^\circ\)
\(\Rightarrow\min\left(x\right)=?\)
Property 9
\(m\left(\widehat{A}\right)>m\left(\widehat{B}\right)>m\left(\widehat{C}\right)\)
\(\mathrm{1)}\quad a>b>c\)
\(\mathrm{2)}\quad h_a<h_b<h_c\)
\(\mathrm{3)}\quad n_A<n_B<n_C\)
\(\mathrm{4)}\quad V_a<V_b<V_c\)
h: (height)
n: (bisector)
V: (median)
1.
\(h_a,h_b,h_c\)
\(\Rightarrow ?>?>?\)
2.
ABC equilateral triangle
\(V_x,V_y,V_z\)
\(\Rightarrow ?>?>?\)
3.
\(m\left(\widehat{DAC}\right)=60^\circ\)
\(n_A,n_B,n_C\)
\(\Rightarrow ?>?>?\)