В треугольнике со сторонами: a = 4.6, b = 5.7, с = 3.431, углы равны α° = 53.79°, β° = 88.36°, γ° = 37°
Ответ:
a=4.6
b=5.7
c=3.431
α°=53.79°
β°=88.36°
γ°=37°
S = 7.894
ha=3.432
hb=2.77
hc=4.602
P = 13.73
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √4.62 + 5.72 - 2·4.6·5.7·cos(37°)
= √21.16 + 32.49 - 52.44·0.7986
= √11.77
= 3.431
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
4.6
3.431
sin(37°))
= arcsin(1.341·0.6018)
= 53.81°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
5.72+3.4312-4.62
2·5.7·3.431
)
= arccos(
32.49+11.771761-21.16
39.11
)
= 53.79°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
5.7
3.431
sin(37°))
= arcsin(1.661·0.6018)
= 88.36°
Периметр:
P = a + b + c
= 4.6 + 5.7 + 3.431
= 13.73
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√6.866·(6.866-4.6)·(6.866-5.7)·(6.866-3.431)
=√6.866 · 2.266 · 1.166 · 3.435
=√62.31448303476
= 7.894
Высота :
ha =
2S
a
=
2 · 7.894
4.6
= 3.432
hb =
2S
b
=
2 · 7.894
5.7
= 2.77
hc =
2S
c
=
2 · 7.894
3.431
= 4.602