В треугольнике со сторонами: a = 3, b = 1, с = 2.646, углы равны α° = 100.88°, β° = 19.1°, γ° = 60°
Ответ:
a=3
b=1
c=2.646
α°=100.88°
β°=19.1°
γ°=60°
S = 1.299
ha=0.866
hb=2.598
hc=0.9819
P = 6.646
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √32 + 12 - 2·3·1·cos(60°)
= √9 + 1 - 6·0.5
= √7
= 2.646
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
3
2.646
sin(60°))
= arcsin(1.134·0.866)
= 79.13°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
12+2.6462-32
2·1·2.646
)
= arccos(
1+7.001316-9
5.292
)
= 100.88°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
1
2.646
sin(60°))
= arcsin(0.3779·0.866)
= 19.1°
Периметр:
P = a + b + c
= 3 + 1 + 2.646
= 6.646
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√3.323·(3.323-3)·(3.323-1)·(3.323-2.646)
=√3.323 · 0.323 · 2.323 · 0.677
=√1.687993391759
= 1.299
Высота :
ha =
2S
a
=
2 · 1.299
3
= 0.866
hb =
2S
b
=
2 · 1.299
1
= 2.598
hc =
2S
c
=
2 · 1.299
2.646
= 0.9819