Решение:
Угол:
α° = arccos(
)
= arccos(
10.832+9.312-11.22
2·10.83·9.31
)
= arccos(
117.2889+86.6761-125.44
201.65
)
= 67.08°
Периметр:
P = a + b + c
= 11.2 + 10.83 + 9.31
= 31.34
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√15.67·(15.67-11.2)·(15.67-10.83)·(15.67-9.31)
=√15.67 · 4.47 · 4.84 · 6.36
=√2156.15012976
= 46.43
Высота :
ha =
=
= 8.291
hb =
=
= 8.574
hc =
=
= 9.974
Угол:
β° = arcsin(
sin(α°))
= arcsin(
sin(67.08°))
= arcsin(0.967·0.921)
= 62.95°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(67.08°))
= arcsin(0.8313·0.921)
= 49.96°