Решение:
Угол:
α° = arccos(
)
= arccos(
6.3245553203367592+4.472135954999582-7.2111025509279782
2·6.324555320336759·4.47213595499958
)
= arccos(
)
= 81.87°
Периметр:
P = a + b + c
= 7.211102550927978 + 6.324555320336759 + 4.47213595499958
= 18.01
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√9.004·(9.004-7.211102550927978)·(9.004-6.324555320336759)·(9.004-4.47213595499958)
=√9.004 · 1.792897449072 · 2.6794446796632 · 4.5318640450004
=√196.0255148685
= 14
Высота :
ha =
=
= 3.883
hb =
=
= 4.427
hc =
=
= 6.261
Угол:
β° = arcsin(
sin(α°))
= arcsin(
6.324555320336759
7.211102550927978
sin(81.87°))
= arcsin(0.8771·0.9899)
= 60.25°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
4.47213595499958
7.211102550927978
sin(81.87°))
= arcsin(0.6202·0.9899)
= 37.87°