В треугольнике со сторонами: a = 5.5, b = 5.5, с = 8.426, углы равны α° = 40.01°, β° = 40°, γ° = 100°
Ответ:
a=5.5
b=5.5
c=8.426
α°=40.01°
β°=40°
γ°=100°
S = 14.9
ha=5.418
hb=5.418
hc=3.537
P = 19.43
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √5.52 + 5.52 - 2·5.5·5.5·cos(100°)
= √30.25 + 30.25 - 60.5·-0.1736
= √71
= 8.426
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
5.5
8.426
sin(100°))
= arcsin(0.6527·0.9848)
= 40°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
5.52+8.4262-5.52
2·5.5·8.426
)
= arccos(
30.25+70.997476-30.25
92.69
)
= 40.01°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
5.5
8.426
sin(100°))
= arcsin(0.6527·0.9848)
= 40°
Периметр:
P = a + b + c
= 5.5 + 5.5 + 8.426
= 19.43
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√9.713·(9.713-5.5)·(9.713-5.5)·(9.713-8.426)
=√9.713 · 4.213 · 4.213 · 1.287
=√221.87831235184
= 14.9
Высота :
ha =
2S
a
=
2 · 14.9
5.5
= 5.418
hb =
2S
b
=
2 · 14.9
5.5
= 5.418
hc =
2S
c
=
2 · 14.9
8.426
= 3.537