Решение:
Угол:
α° = arccos(
)
= arccos(
)
= arccos(
)
= 89.41°
Периметр:
P = a + b + c
= 85 + 67 + 53
= 205
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√102.5·(102.5-85)·(102.5-67)·(102.5-53)
=√102.5 · 17.5 · 35.5 · 49.5
=√3152067.1875
= 1775.4
Высота :
ha =
=
= 41.77
hb =
=
= 53
hc =
=
= 67
Угол:
β° = arcsin(
sin(α°))
= arcsin(
sin(89.41°))
= arcsin(0.7882·0.9999)
= 52.01°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(89.41°))
= arcsin(0.6235·0.9999)
= 38.57°