В треугольнике со сторонами: a = 10, b = 2, с = 9.165, углы равны α° = 109.11°, β° = 10.89°, γ° = 60°
Ответ:
a=10
b=2
c=9.165
α°=109.11°
β°=10.89°
γ°=60°
S = 8.631
ha=1.726
hb=8.631
hc=1.883
P = 21.17
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √102 + 22 - 2·10·2·cos(60°)
= √100 + 4 - 40·0.5
= √84
= 9.165
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
10
9.165
sin(60°))
= arcsin(1.091·0.866)
= 70.87°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
22+9.1652-102
2·2·9.165
)
= arccos(
4+83.997225-100
36.66
)
= 109.11°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
2
9.165
sin(60°))
= arcsin(0.2182·0.866)
= 10.89°
Периметр:
P = a + b + c
= 10 + 2 + 9.165
= 21.17
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√10.58·(10.58-10)·(10.58-2)·(10.58-9.165)
=√10.58 · 0.58 · 8.58 · 1.415
=√74.50019148
= 8.631
Высота :
ha =
2S
a
=
2 · 8.631
10
= 1.726
hb =
2S
b
=
2 · 8.631
2
= 8.631
hc =
2S
c
=
2 · 8.631
9.165
= 1.883