Решение:
Угол:
α° = arccos(
)
= arccos(
10.832+11.22-9.312
2·10.83·11.2
)
= arccos(
117.2889+125.44-86.6761
242.59
)
= 49.96°
Периметр:
P = a + b + c
= 9.31 + 10.83 + 11.2
= 31.34
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√15.67·(15.67-9.31)·(15.67-10.83)·(15.67-11.2)
=√15.67 · 6.36 · 4.84 · 4.47
=√2156.15012976
= 46.43
Высота :
ha =
=
= 9.974
hb =
=
= 8.574
hc =
=
= 8.291
Угол:
β° = arcsin(
sin(α°))
= arcsin(
sin(49.96°))
= arcsin(1.163·0.7656)
= 62.92°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(49.96°))
= arcsin(1.203·0.7656)
= 67.08°