В треугольнике со сторонами: a = 5.874, b = 5.874, с = 9 высоты равны ha = 2.5, hb = 5.771, hc = 3.767
Ответ:
a=5.874
b=5.874
c=9
α°=40°
β°=40°
γ°=100°
S = 16.95
ha=2.5
hb=5.771
hc=3.767
P = 20.75
Решение:
Угол:
γ° = 180 - α° - β°
= 180 - 40° - 40°
= 100°
Сторона:
a = c·
sin(α°)
sin(γ°)
= 9·
sin(40°)
sin(100°)
= 9·
0.6428
0.9848
= 9·0.6527
= 5.874
Сторона:
b = c·
sin(β°)
sin(γ°)
= 9·
sin(40°)
sin(100°)
= 9·
0.6428
0.9848
= 9·0.6527
= 5.874
Периметр:
P = a + b + c
= 5.874 + 5.874 + 9
= 20.75
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√10.37·(10.37-5.874)·(10.37-5.874)·(10.37-9)
=√10.37 · 4.496 · 4.496 · 1.37
=√287.1785039104
= 16.95
hb =
2S
b
=
2 · 16.95
5.874
= 5.771
hc =
2S
c
=
2 · 16.95
9
= 3.767