В треугольнике со сторонами: a = 78.81, b = 45.5, с = 45.5, углы равны α° = 120°, β° = 30°, γ° = 30°
Ответ:
a=78.81
b=45.5
c=45.5
α°=120°
β°=30°
γ°=30°
S = 896.91
ha=22.76
hb=39.42
hc=39.42
P = 169.81
Решение:
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √45.52 + 45.52 - 2·45.5·45.5·cos(120°)
= √2070.3 + 2070.3 - 4140.5·-0.5
= √6210.9
= 78.81
или:
a = b·
sin(α°)
sin(β°)
= 45.5·
sin(120°)
sin(30°)
= 45.5·
0.866
0.5
= 45.5·1.732
= 78.81
или:
a = c·
sin(α°)
sin(γ°)
= 45.5·
sin(120°)
sin(30°)
= 45.5·
0.866
0.5
= 45.5·1.732
= 78.81
Периметр:
P = a + b + c
= 78.81 + 45.5 + 45.5
= 169.81
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√84.91·(84.91-78.81)·(84.91-45.5)·(84.91-45.5)
=√84.91 · 6.1 · 39.41 · 39.41
=√804454.6115431
= 896.91
Высота :
ha =
2S
a
=
2 · 896.91
78.81
= 22.76
hb =
2S
b
=
2 · 896.91
45.5
= 39.42
hc =
2S
c
=
2 · 896.91
45.5
= 39.42