Решение:
Сторона:
b = √a2 + c2 - 2ac·cos(β°)
= √18002 + 5002 - 2·1800·500·cos(91°)
= √3240000 + 250000 - 1800000·-0.01745
= √3521410
= 1876.5
Высота :
hc = a·sin(β°)
= 1800·sin(91°)
= 1800·0.9998
= 1799.6
Угол:
α° = arcsin(
sin(β°))
= arcsin(
sin(91°))
= arcsin(0.9592·0.9998)
= 73.54°
или:
α° = arccos(
)
= arccos(
1876.52+5002-18002
2·1876.5·500
)
= arccos(
3521252.25+250000-3240000
1876500
)
= 73.55°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(91°))
= arcsin(0.2665·0.9998)
= 15.45°
Периметр:
P = a + b + c
= 1800 + 1876.5 + 500
= 4176.5
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√2088.3·(2088.3-1800)·(2088.3-1876.5)·(2088.3-500)
=√2088.3 · 288.3 · 211.8 · 1588.3
=√202533105786.37
= 450036.8
Высота :
ha =
=
= 500.04
hb =
=
= 479.66