Решение:
Сторона:
b = √a2 + c2 - 2ac·cos(β°)
= √2552 + 1902 - 2·255·190·cos(45°)
= √65025 + 36100 - 96900·0.7071
= √32607
= 180.57
Высота :
hc = a·sin(β°)
= 255·sin(45°)
= 255·0.7071
= 180.31
Угол:
α° = arcsin(
sin(β°))
= arcsin(
sin(45°))
= arcsin(1.412·0.7071)
= 86.78°
или:
α° = arccos(
)
= arccos(
180.572+1902-2552
2·180.57·190
)
= arccos(
32605.5249+36100-65025
68616.6
)
= 86.93°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(45°))
= arcsin(1.052·0.7071)
= 48.06°
Периметр:
P = a + b + c
= 255 + 180.57 + 190
= 625.57
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√312.79·(312.79-255)·(312.79-180.57)·(312.79-190)
=√312.79 · 57.79 · 132.22 · 122.79
=√293471347.8817
= 17131
hb =
=
= 189.74