В треугольнике со сторонами: a = 3.3, b = 5.35, с = 7.561, углы равны α° = 22.2°, β° = 37.79°, γ° = 120°
Ответ:
a=3.3
b=5.35
c=7.561
α°=22.2°
β°=37.79°
γ°=120°
S = 7.649
ha=1.5
hb=2.859
hc=2.023
P = 16.21
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √3.32 + 5.352 - 2·3.3·5.35·cos(120°)
= √10.89 + 28.62 - 35.31·-0.5
= √57.17
= 7.561
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
3.3
7.561
sin(120°))
= arcsin(0.4365·0.866)
= 22.21°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
5.352+7.5612-3.32
2·5.35·7.561
)
= arccos(
28.6225+57.168721-10.89
80.9
)
= 22.2°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
5.35
7.561
sin(120°))
= arcsin(0.7076·0.866)
= 37.79°
Периметр:
P = a + b + c
= 3.3 + 5.35 + 7.561
= 16.21
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√8.106·(8.106-3.3)·(8.106-5.35)·(8.106-7.561)
=√8.106 · 4.806 · 2.756 · 0.545
=√58.51484802072
= 7.649
hb =
2S
b
=
2 · 7.649
5.35
= 2.859
hc =
2S
c
=
2 · 7.649
7.561
= 2.023