26.
[tex]\it cosA=\dfrac{AB^2+AC^2-BC^2}{2\cdot AB\cdot AC}=\dfrac{8^2+6^2-(2\sqrt{37})^2}{2\cdot8\cdot6}=\dfrac{64+36-148}{2\cdot48}=\\ \\ \\ =-\dfrac{48}{2\cdot48}=-\dfrac{1}{2} \Rightarrow m(\hat A)=120^o\\ \\ \\ sin A=sin120^o=\dfrac{\sqrt3}{2}[/tex]
27.
[tex]\it S=\dfrac{AB\cdot BC\cdot sin135^o}{2}=\dfrac{7\cdot4\cdot\dfrac{\sqrt2}{2}}{2}=7\sqrt2[/tex]
28.
[tex]\it sinC=\sqrt{1-cos^2C}=\sqrt{1-\Big(\dfrac{3}{5}\Big)^2}=\sqrt{\dfrac{16}{25}}=\dfrac{4}{5}\\ \\ \\ S=\dfrac{AC\cdot BC\cdot sinC}{2}=\dfrac{10\cdot8\cdot\dfrac{4}{5}}{2}=32[/tex]
