Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √22 + 5.196152422 - 2·2·5.19615242·cos(150°)
= √4 + 27 - 20.78·-0.866
= √49
= 7
Угол:
α° = arcsin(
sin(γ°))
= arcsin(
sin(150°))
= arcsin(0.2857·0.5)
= 8.213°
или:
α° = arccos(
)
= arccos(
5.196152422+72-22
2·5.19615242·7
)
= arccos(
26.999999971872+49-4
72.75
)
= 8.234°
Угол:
β° = arcsin(
sin(γ°))
= arcsin(
sin(150°))
= arcsin(0.7423·0.5)
= 21.79°
Периметр:
P = a + b + c
= 2 + 5.19615242 + 7
= 14.2
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√7.098·(7.098-2)·(7.098-5.19615242)·(7.098-7)
=√7.098 · 5.098 · 1.90184758 · 0.098
=√6.7443113330273
= 2.597
Высота :
ha =
=
= 2.597
hb =
=
= 0.9996
hc =
=
= 0.742