В треугольнике со сторонами: a = 1, b = 3, с = 3.606, углы равны α° = 13.93°, β° = 46.09°, γ° = 120°
Ответ:
a=1
b=3
c=3.606
α°=13.93°
β°=46.09°
γ°=120°
S = 1.299
ha=2.598
hb=0.866
hc=0.7205
P = 7.606
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √12 + 32 - 2·1·3·cos(120°)
= √1 + 9 - 6·-0.5
= √13
= 3.606
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
1
3.606
sin(120°))
= arcsin(0.2773·0.866)
= 13.89°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
32+3.6062-12
2·3·3.606
)
= arccos(
9+13.003236-1
21.64
)
= 13.93°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
3
3.606
sin(120°))
= arcsin(0.8319·0.866)
= 46.09°
Периметр:
P = a + b + c
= 1 + 3 + 3.606
= 7.606
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√3.803·(3.803-1)·(3.803-3)·(3.803-3.606)
=√3.803 · 2.803 · 0.803 · 0.197
=√1.686285845519
= 1.299
Высота :
ha =
2S
a
=
2 · 1.299
1
= 2.598
hb =
2S
b
=
2 · 1.299
3
= 0.866
hc =
2S
c
=
2 · 1.299
3.606
= 0.7205