Решение:
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √18002 + 5002 - 2·1800·500·cos(88°)
= √3240000 + 250000 - 1800000·0.0349
= √3427180
= 1851.3
Угол:
β° = arcsin(
sin(α°))
= arcsin(
sin(88°))
= arcsin(0.9723·0.9994)
= 76.34°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(88°))
= arcsin(0.2701·0.9994)
= 15.66°
Периметр:
P = a + b + c
= 1851.3 + 1800 + 500
= 4151.3
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√2075.7·(2075.7-1851.3)·(2075.7-1800)·(2075.7-500)
=√2075.7 · 224.4 · 275.7 · 1575.7
=√202347451529.27
= 449830.5
Высота :
ha =
=
= 485.96
hb =
=
= 499.81
hc =
=
= 1799.3