Решение:
Угол:
α° = arcsin(
sin(γ°))
= arcsin(
sin(50°))
= arcsin(1·0.766)
= 50°
Угол:
β° = 180 - γ° - α°
= 180 - 50° - 50°
= 80°
Сторона:
b = √a2 + c2 - 2ac·cos(β°)
= √332 + 332 - 2·33·33·cos(80°)
= √1089 + 1089 - 2178·0.1736
= √1799.9
= 42.43
или:
b = a·
= 33·
= 33·
= 33·1.286
= 42.44
или:
b = c·
= 33·
= 33·
= 33·1.286
= 42.44
Высота :
hc = a·sin(β°)
= 33·sin(80°)
= 33·0.9848
= 32.5
Периметр:
P = a + b + c
= 33 + 42.44 + 33
= 108.44
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√54.22·(54.22-33)·(54.22-42.44)·(54.22-33)
=√54.22 · 21.22 · 11.78 · 21.22
=√287604.42442544
= 536.29
Высота :
ha =
=
= 32.5
hb =
=
= 25.27