Решение:
Сторона:
b = √a2 + c2 - 2ac·cos(β°)
= √1.62 + 1.62 - 2·1.6·1.6·cos(80°)
= √2.56 + 2.56 - 5.12·0.1736
= √4.231
= 2.057
Высота :
hc = a·sin(β°)
= 1.6·sin(80°)
= 1.6·0.9848
= 1.576
Угол:
α° = arcsin(
sin(β°))
= arcsin(
sin(80°))
= arcsin(0.7778·0.9848)
= 49.99°
или:
α° = arccos(
)
= arccos(
2.0572+1.62-1.62
2·2.057·1.6
)
= arccos(
)
= 50°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(80°))
= arcsin(0.7778·0.9848)
= 49.99°
Периметр:
P = a + b + c
= 1.6 + 2.057 + 1.6
= 5.257
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√2.629·(2.629-1.6)·(2.629-2.057)·(2.629-1.6)
=√2.629 · 1.029 · 0.572 · 1.029
=√1.592272389708
= 1.262
Высота :
ha =
=
= 1.578
hb =
=
= 1.227