В треугольнике со сторонами: a = 1.905, b = 1.905, с = 3.3, углы равны α° = 30°, β° = 30°, γ° = 120°
Ответ:
a=1.905
b=1.905
c=3.3
α°=30°
β°=30°
γ°=120°
S = 1.571
ha=1.649
hb=1.649
hc=0.9525
P = 7.11
Решение:
Сторона:
a = c·
sin(α°)
sin(γ°)
= 3.3·
sin(30°)
sin(120°)
= 3.3·
0.5
0.866
= 3.3·0.5774
= 1.905
Угол:
β° = 180 - γ° - α°
= 180 - 120° - 30°
= 30°
Сторона:
b = √a2 + c2 - 2ac·cos(β°)
= √1.9052 + 3.32 - 2·1.905·3.3·cos(30°)
= √3.629 + 10.89 - 12.57·0.866
= √3.633
= 1.906
или:
b = a·
sin(β°)
sin(α°)
= 1.905·
sin(30°)
sin(30°)
= 1.905·
0.5
0.5
= 1.905·1
= 1.905
или:
b = c·
sin(β°)
sin(γ°)
= 3.3·
sin(30°)
sin(120°)
= 3.3·
0.5
0.866
= 3.3·0.5774
= 1.905
Высота :
hc = a·sin(β°)
= 1.905·sin(30°)
= 1.905·0.5
= 0.9525
Периметр:
P = a + b + c
= 1.905 + 1.905 + 3.3
= 7.11
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√3.555·(3.555-1.905)·(3.555-1.905)·(3.555-3.3)
=√3.555 · 1.65 · 1.65 · 0.255
=√2.4680143125
= 1.571
Высота :
ha =
2S
a
=
2 · 1.571
1.905
= 1.649
hb =
2S
b
=
2 · 1.571
1.905
= 1.649