В треугольнике со сторонами: a = 3.3, b = 5.35, с = 8.158, углы равны α° = 15.08°, β° = 24.93°, γ° = 140°
Ответ:
a=3.3
b=5.35
c=8.158
α°=15.08°
β°=24.93°
γ°=140°
S = 5.677
ha=1.5
hb=2.122
hc=1.392
P = 16.81
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √3.32 + 5.352 - 2·3.3·5.35·cos(140°)
= √10.89 + 28.62 - 35.31·-0.766
= √66.56
= 8.158
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
3.3
8.158
sin(140°))
= arcsin(0.4045·0.6428)
= 15.07°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
5.352+8.1582-3.32
2·5.35·8.158
)
= arccos(
28.6225+66.552964-10.89
87.29
)
= 15.08°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
5.35
8.158
sin(140°))
= arcsin(0.6558·0.6428)
= 24.93°
Периметр:
P = a + b + c
= 3.3 + 5.35 + 8.158
= 16.81
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√8.404·(8.404-3.3)·(8.404-5.35)·(8.404-8.158)
=√8.404 · 5.104 · 3.054 · 0.246
=√32.225587916544
= 5.677
hb =
2S
b
=
2 · 5.677
5.35
= 2.122
hc =
2S
c
=
2 · 5.677
8.158
= 1.392