Oblicz sin a,b,y i c

[winfast29]

Mając dane a=6, b=10, R=8. Oblicz sina, sinb, siny i c.

[meninio]

Skorzystaj z twierdzenia sinusów:

\(\displaystyle{ \frac{a}{\sin }=\frac{b}{\sin \beta}=\frac{c}{\sin \gamma}=2R}\)

[wb]

\(\displaystyle{ \frac{a}{sin\alpha}=2R sin\alpha= \frac{6}{2 8}= \frac{3}{8} \\ \\ \frac{b}{sin\beta}=2R sin\beta= \frac{10}{2 8}= \frac{5}{8} \\ \\ sin\alpha= \frac{3}{8} cos\alpha= \sqrt{1- (\frac{3}{8)^2} }= \frac{\sqrt{55}}{8} \\ \\ 6^2=c^2+10^2-2 10 c cos\alpha \\ 36=c^2+100-20 \frac{\sqrt{55}}{8}c \\ \\ ...}\)