В треугольнике со сторонами: a = 159.81, b = 116.8, с = 178, углы равны α° = 61.58°, β° = 40°, γ° = 78.42°
Ответ:
a=159.81
b=116.8
c=178
α°=61.58°
β°=40°
γ°=78.42°
S = 9143.9
ha=114.43
hb=156.57
hc=102.74
P = 454.61
Решение:
Угол:
γ° = 180 - α° - β°
= 180 - 61.58° - 40°
= 78.42°
Сторона:
a = c·
sin(α°)
sin(γ°)
= 178·
sin(61.58°)
sin(78.42°)
= 178·
0.8795
0.9796
= 178·0.8978
= 159.81
Сторона:
b = c·
sin(β°)
sin(γ°)
= 178·
sin(40°)
sin(78.42°)
= 178·
0.6428
0.9796
= 178·0.6562
= 116.8
Периметр:
P = a + b + c
= 159.81 + 116.8 + 178
= 454.61
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√227.31·(227.31-159.81)·(227.31-116.8)·(227.31-178)
=√227.31 · 67.5 · 110.51 · 49.31
=√83610129.528743
= 9143.9
Высота :
ha =
2S
a
=
2 · 9143.9
159.81
= 114.43
hb =
2S
b
=
2 · 9143.9
116.8
= 156.57
hc =
2S
c
=
2 · 9143.9
178
= 102.74