В треугольнике со сторонами: a = 8.001, b = 13, с = 7, углы равны α° = 32.2°, β° = 120°, γ° = 27.8°
Ответ:
a=8.001
b=13
c=7
α°=32.2°
β°=120°
γ°=27.8°
S = 24.25
ha=6.062
hb=3.731
hc=6.929
P = 28
Решение:
Угол:
γ° = arcsin(
c
b
sin(α°))
= arcsin(
7
13
sin(120°))
= arcsin(0.5385·0.866)
= 27.8°
Угол:
α° = 180 - γ° - β°
= 180 - 27.8° - 120°
= 32.2°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √132 + 72 - 2·13·7·cos(32.2°)
= √169 + 49 - 182·0.8462
= √63.99
= 7.999
или:
a = b·
sin(α°)
sin(β°)
= 13·
sin(32.2°)
sin(120°)
= 13·
0.5329
0.866
= 13·0.6154
= 8
или:
a = c·
sin(α°)
sin(γ°)
= 7·
sin(32.2°)
sin(27.8°)
= 7·
0.5329
0.4664
= 7·1.143
= 8.001
Периметр:
P = a + b + c
= 8.001 + 13 + 7
= 28
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√14·(14-8.001)·(14-13)·(14-7)
=√14 · 5.999 · 1 · 7
=√587.902
= 24.25
Высота :
ha =
2S
a
=
2 · 24.25
8.001
= 6.062
hb =
2S
b
=
2 · 24.25
13
= 3.731
hc =
2S
c
=
2 · 24.25
7
= 6.929