В треугольнике со сторонами: a = 17.89, b = 17.89, с = 30 высоты равны ha = 16.35, hb = 16.35, hc = 9.749
Ответ:
a=17.89
b=17.89
c=30
α°=33°
β°=33°
γ°=114°
S = 146.24
ha=16.35
hb=16.35
hc=9.749
P = 65.78
Решение:
Угол:
γ° = 180 - α° - β°
= 180 - 33° - 33°
= 114°
Сторона:
a = c·
sin(α°)
sin(γ°)
= 30·
sin(33°)
sin(114°)
= 30·
0.5446
0.9135
= 30·0.5962
= 17.89
Сторона:
b = c·
sin(β°)
sin(γ°)
= 30·
sin(33°)
sin(114°)
= 30·
0.5446
0.9135
= 30·0.5962
= 17.89
Периметр:
P = a + b + c
= 17.89 + 17.89 + 30
= 65.78
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√32.89·(32.89-17.89)·(32.89-17.89)·(32.89-30)
=√32.89 · 15 · 15 · 2.89
=√21386.7225
= 146.24
Высота :
ha =
2S
a
=
2 · 146.24
17.89
= 16.35
hb =
2S
b
=
2 · 146.24
17.89
= 16.35
hc =
2S
c
=
2 · 146.24
30
= 9.749