22.C
Công thức đúng là \(\dfrac{b}{sinB}=2R\)
23.
\(R=\dfrac{BC}{2sin\widehat{BAC}}=\dfrac{\sqrt{3}}{2sin60^0}=1\)
24.
Áp dụng định lý sín:
\(\dfrac{AC}{sinB}=\dfrac{BC}{sinA}\Rightarrow BC=\dfrac{AC.sinA}{sinB}=\dfrac{4.sin60^0}{sin45^0}=2\sqrt{6}\)
25.
\(C=180^0-\left(A+B\right)=80^0\)
Áp dụng định lý sin:
\(\dfrac{BC}{sinA}=\dfrac{AB}{sinC}\Rightarrow BC=\dfrac{AB.sinA}{sinC}=\dfrac{5.sin40^0}{sin80^0}=3,3\)
26.
\(\dfrac{a}{sinA}=\dfrac{b}{sinB}=\dfrac{c}{sinC}=2R\Rightarrow\left\{{}\begin{matrix}a=2R.sinA\\b=2R.sinB\\c=2R.sinC\end{matrix}\right.\)
\(\Rightarrow2R.sinB+2R.sinC=2.2R.sinA\)
\(\Rightarrow sinB+sinC=2sinA\)
27.
\(A=180^0-\left(B+C\right)=52^047'\)
\(\dfrac{a}{sinA}=\dfrac{c}{sinC}\Rightarrow c=\dfrac{a.sinC}{sinA}=19,9\)
28.
\(C=180^0-\left(A+B\right)=77^04'\)
\(\dfrac{AB}{sinC}=\dfrac{AC}{sinB}\Rightarrow AC=\dfrac{AB.sinB}{sinC}=68\)
