10. 5 sin (π/2 + arccos 3/7)

1) $$arccos(\frac{3}{7}) = a$$

2) $$sin(\frac{\pi}{2} + a) = cos(a)$$

3) $$cos(a) = cos(arccos(\frac{3}{7})) = \frac{3}{7}$$

4) $$5 \cdot \frac{3}{7} = \frac{15}{7}$$

Ответ: $$\frac{15}{7}$$