Решение:
Угол:
α° = arccos(
)
= arccos(
5.19615242272+8.66025403782-12.1243556532
2·5.1961524227·8.6602540378
)
= arccos(
26.999999999931+74.999999999231-147.00000000043
90
)
= 120°
Периметр:
P = a + b + c
= 12.124355653 + 5.1961524227 + 8.6602540378
= 25.98
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√12.99·(12.99-12.124355653)·(12.99-5.1961524227)·(12.99-8.6602540378)
=√12.99 · 0.865644347 · 7.7938475773 · 4.3297459622
=√379.45735254746
= 19.48
Высота :
ha =
=
= 3.213
hb =
=
= 7.498
hc =
=
= 4.499
Угол:
β° = arcsin(
sin(α°))
= arcsin(
sin(120°))
= arcsin(0.4286·0.866)
= 21.79°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(120°))
= arcsin(0.7143·0.866)
= 38.21°