В треугольнике со сторонами: a = 2, b = 1.7, с = 3.575, углы равны α° = 16.31°, β° = 13.75°, γ° = 150°
Ответ:
a=2
b=1.7
c=3.575
α°=16.31°
β°=13.75°
γ°=150°
S = 0.853
ha=0.853
hb=1.004
hc=0.4772
P = 7.275
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √22 + 1.72 - 2·2·1.7·cos(150°)
= √4 + 2.89 - 6.8·-0.866
= √12.78
= 3.575
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
2
3.575
sin(150°))
= arcsin(0.5594·0.5)
= 16.24°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
1.72+3.5752-22
2·1.7·3.575
)
= arccos(
2.89+12.780625-4
12.16
)
= 16.31°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
1.7
3.575
sin(150°))
= arcsin(0.4755·0.5)
= 13.75°
Периметр:
P = a + b + c
= 2 + 1.7 + 3.575
= 7.275
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√3.638·(3.638-2)·(3.638-1.7)·(3.638-3.575)
=√3.638 · 1.638 · 1.938 · 0.063
=√0.727563518136
= 0.853
Высота :
ha =
2S
a
=
2 · 0.853
2
= 0.853
hb =
2S
b
=
2 · 0.853
1.7
= 1.004
hc =
2S
c
=
2 · 0.853
3.575
= 0.4772