Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √115.562 + 1162 - 2·115.56·116·cos(9.5°)
= √13354.1 + 13456 - 26809.9·0.9863
= √367.5
= 19.17
Угол:
α° = arcsin(
sin(γ°))
= arcsin(
sin(9.5°))
= arcsin(6.028·0.165)
= 84.05°
или:
α° = arccos(
)
= arccos(
1162+19.172-115.562
2·116·19.17
)
= arccos(
13456+367.4889-13354.1136
4447.4
)
= 83.94°
Угол:
β° = arcsin(
sin(γ°))
= arcsin(
sin(9.5°))
= arcsin(6.051·0.165)
= 86.77°
Периметр:
P = a + b + c
= 115.56 + 116 + 19.17
= 250.73
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√125.37·(125.37-115.56)·(125.37-116)·(125.37-19.17)
=√125.37 · 9.81 · 9.37 · 106.2
=√1223845.9101918
= 1106.3
Высота :
ha =
=
= 19.15
hb =
=
= 19.07
hc =
=
= 115.42