В треугольнике со сторонами: a = 3.266, b = 1.195, с = 4 высоты равны ha = 1.036, hb = 2.832, hc = 0.846
Ответ:
a=3.266
b=1.195
c=4
α°=45°
β°=15°
γ°=120°
S = 1.692
ha=1.036
hb=2.832
hc=0.846
P = 8.461
Решение:
Угол:
γ° = 180 - α° - β°
= 180 - 45° - 15°
= 120°
Сторона:
a = c·
sin(α°)
sin(γ°)
= 4·
sin(45°)
sin(120°)
= 4·
0.7071
0.866
= 4·0.8165
= 3.266
Сторона:
b = c·
sin(β°)
sin(γ°)
= 4·
sin(15°)
sin(120°)
= 4·
0.2588
0.866
= 4·0.2988
= 1.195
Периметр:
P = a + b + c
= 3.266 + 1.195 + 4
= 8.461
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√4.231·(4.231-3.266)·(4.231-1.195)·(4.231-4)
=√4.231 · 0.965 · 3.036 · 0.231
=√2.86341361614
= 1.692
Высота :
ha =
2S
a
=
2 · 1.692
3.266
= 1.036
hb =
2S
b
=
2 · 1.692
1.195
= 2.832
hc =
2S
c
=
2 · 1.692
4
= 0.846