Решение:
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √18002 + 5002 - 2·1800·500·cos(92°)
= √3240000 + 250000 - 1800000·-0.0349
= √3552820
= 1884.9
Угол:
β° = arcsin(
sin(α°))
= arcsin(
sin(92°))
= arcsin(0.955·0.9994)
= 72.64°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(92°))
= arcsin(0.2653·0.9994)
= 15.38°
Периметр:
P = a + b + c
= 1884.9 + 1800 + 500
= 4184.9
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√2092.5·(2092.5-1884.9)·(2092.5-1800)·(2092.5-500)
=√2092.5 · 207.6 · 292.5 · 1592.5
=√202347632418.75
= 449830.7
Высота :
ha =
=
= 477.3
hb =
=
= 499.81
hc =
=
= 1799.3