В треугольнике со сторонами: a = 5.7, b = 1.5, с = 4.464, углы равны α° = 140.37°, β° = 9.672°, γ° = 30°
Ответ:
a=5.7
b=1.5
c=4.464
α°=140.37°
β°=9.672°
γ°=30°
S = 2.136
ha=0.7495
hb=2.848
hc=0.957
P = 11.66
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √5.72 + 1.52 - 2·5.7·1.5·cos(30°)
= √32.49 + 2.25 - 17.1·0.866
= √19.93
= 4.464
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
5.7
4.464
sin(30°))
= arcsin(1.277·0.5)
= 39.68°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
1.52+4.4642-5.72
2·1.5·4.464
)
= arccos(
2.25+19.927296-32.49
13.39
)
= 140.37°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
1.5
4.464
sin(30°))
= arcsin(0.336·0.5)
= 9.672°
Периметр:
P = a + b + c
= 5.7 + 1.5 + 4.464
= 11.66
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√5.832·(5.832-5.7)·(5.832-1.5)·(5.832-4.464)
=√5.832 · 0.132 · 4.332 · 1.368
=√4.562112513024
= 2.136
Высота :
ha =
2S
a
=
2 · 2.136
5.7
= 0.7495
hb =
2S
b
=
2 · 2.136
1.5
= 2.848
hc =
2S
c
=
2 · 2.136
4.464
= 0.957