В треугольнике со сторонами: a = 59.16, b = 114.66, с = 70 высоты равны ha = 57.36, hb = 29.6, hc = 48.48
Ответ:
a=59.16
b=114.66
c=70
α°=25°
β°=125°
γ°=30°
S = 1696.8
ha=57.36
hb=29.6
hc=48.48
P = 243.82
Решение:
Угол:
γ° = 180 - α° - β°
= 180 - 25° - 125°
= 30°
Сторона:
a = c·
sin(α°)
sin(γ°)
= 70·
sin(25°)
sin(30°)
= 70·
0.4226
0.5
= 70·0.8452
= 59.16
Сторона:
b = c·
sin(β°)
sin(γ°)
= 70·
sin(125°)
sin(30°)
= 70·
0.8192
0.5
= 70·1.638
= 114.66
Периметр:
P = a + b + c
= 59.16 + 114.66 + 70
= 243.82
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√121.91·(121.91-59.16)·(121.91-114.66)·(121.91-70)
=√121.91 · 62.75 · 7.25 · 51.91
=√2879002.8637437
= 1696.8
Высота :
ha =
2S
a
=
2 · 1696.8
59.16
= 57.36
hb =
2S
b
=
2 · 1696.8
114.66
= 29.6
hc =
2S
c
=
2 · 1696.8
70
= 48.48