Решение:
Сторона:
b = √a2 + c2 - 2ac·cos(β°)
= √5002 + 5002 - 2·500·500·cos(101°)
= √250000 + 250000 - 500000·-0.1908
= √595400
= 771.62
Высота :
hc = a·sin(β°)
= 500·sin(101°)
= 500·0.9816
= 490.8
Угол:
α° = arcsin(
sin(β°))
= arcsin(
sin(101°))
= arcsin(0.648·0.9816)
= 39.5°
или:
α° = arccos(
)
= arccos(
771.622+5002-5002
2·771.62·500
)
= arccos(
595397.4244+250000-250000
771620
)
= 39.5°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(101°))
= arcsin(0.648·0.9816)
= 39.5°
Периметр:
P = a + b + c
= 500 + 771.62 + 500
= 1771.6
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√885.81·(885.81-500)·(885.81-771.62)·(885.81-500)
=√885.81 · 385.81 · 114.19 · 385.81
=√15056208213.615
= 122703.7
Высота :
ha =
=
= 490.81
hb =
=
= 318.04