В треугольнике со сторонами: a = 6.306, b = 5.7, с = 8.5, углы равны α° = 47.89°, β° = 42.11°, γ° = 90°
Ответ:
a=6.306
b=5.7
c=8.5
α°=47.89°
β°=42.11°
γ°=90°
S = 17.94
ha=3
hb=6.295
hc=4.221
P = 20.51
Решение:
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
5.7
8.5
sin(90°))
= arcsin(0.6706·1)
= 42.11°
Угол:
α° = 180 - γ° - β°
= 180 - 90° - 42.11°
= 47.89°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √5.72 + 8.52 - 2·5.7·8.5·cos(47.89°)
= √32.49 + 72.25 - 96.9·0.6706
= √39.76
= 6.306
или:
a = b·
sin(α°)
sin(β°)
= 5.7·
sin(47.89°)
sin(42.11°)
= 5.7·
0.7419
0.6706
= 5.7·1.106
= 6.304
или:
a = c·
sin(α°)
sin(γ°)
= 8.5·
sin(47.89°)
sin(90°)
= 8.5·
0.7419
1
= 8.5·0.7419
= 6.306
Периметр:
P = a + b + c
= 6.306 + 5.7 + 8.5
= 20.51
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√10.25·(10.25-6.306)·(10.25-5.7)·(10.25-8.5)
=√10.25 · 3.944 · 4.55 · 1.75
=√321.892025
= 17.94
hb =
2S
b
=
2 · 17.94
5.7
= 6.295
hc =
2S
c
=
2 · 17.94
8.5
= 4.221