Question

Cho ∆ABC vuông tại A ,BC=10cm, AB/AC=3/4 . Tính Sin B ,Sin C

Answer 1

\(\dfrac{AB}{AC}=\dfrac{3}{4}\Leftrightarrow AB=\dfrac{3}{4}AC\)

Ta có \(AB^2+AC^2=\dfrac{9}{16}AC^2+AC^2=BC^2\left(pytago\right)\)

\(\Leftrightarrow\dfrac{25}{16}AC^2=100\Leftrightarrow AC^2=100\cdot\dfrac{16}{25}=64\\ \Leftrightarrow AC=8\left(cm\right)\Leftrightarrow AB=\dfrac{3}{4}\cdot8=6\left(cm\right)\)

\(\sin B=\dfrac{AC}{BC}=\dfrac{4}{5}\\ \sin C=\dfrac{AB}{BC}=\dfrac{3}{5}\)