В треугольнике со сторонами: a = 5.471, b = 7.471, с = 6.7, углы равны α° = 45°, β° = 75°, γ° = 60°
Ответ:
a=5.471
b=7.471
c=6.7
α°=45°
β°=75°
γ°=60°
S = 17.7
ha=1.9
hb=4.738
hc=5.284
P = 19.64
Решение:
Угол:
γ° = 180 - α° - β°
= 180 - 45° - 75°
= 60°
Сторона:
a = c·
sin(α°)
sin(γ°)
= 6.7·
sin(45°)
sin(60°)
= 6.7·
0.7071
0.866
= 6.7·0.8165
= 5.471
Сторона:
b = c·
sin(β°)
sin(γ°)
= 6.7·
sin(75°)
sin(60°)
= 6.7·
0.9659
0.866
= 6.7·1.115
= 7.471
Периметр:
P = a + b + c
= 5.471 + 7.471 + 6.7
= 19.64
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√9.821·(9.821-5.471)·(9.821-7.471)·(9.821-6.7)
=√9.821 · 4.35 · 2.35 · 3.121
=√313.3333333725
= 17.7
hb =
2S
b
=
2 · 17.7
7.471
= 4.738
hc =
2S
c
=
2 · 17.7
6.7
= 5.284