В треугольнике со сторонами: a = 5.5, b = 5.5, с = 10.34, углы равны α° = 20°, β° = 20°, γ° = 140°
Ответ:
a=5.5
b=5.5
c=10.34
α°=20°
β°=20°
γ°=140°
S = 9.701
ha=3
hb=3.528
hc=1.881
P = 21.34
Решение:
Угол:
α° = arcsin(
a
b
sin(β°))
= arcsin(
5.5
5.5
sin(20°))
= arcsin(1·0.342)
= 20°
Высота :
hc = a·sin(β°)
= 5.5·sin(20°)
= 5.5·0.342
= 1.881
Угол:
γ° = 180 - α° - β°
= 180 - 20° - 20°
= 140°
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √5.52 + 5.52 - 2·5.5·5.5·cos(140°)
= √30.25 + 30.25 - 60.5·-0.766
= √106.84
= 10.34
или:
c = a·
sin(γ°)
sin(α°)
= 5.5·
sin(140°)
sin(20°)
= 5.5·
0.6428
0.342
= 5.5·1.88
= 10.34
или:
c = b·
sin(γ°)
sin(β°)
= 5.5·
sin(140°)
sin(20°)
= 5.5·
0.6428
0.342
= 5.5·1.88
= 10.34
Периметр:
P = a + b + c
= 5.5 + 5.5 + 10.34
= 21.34
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√10.67·(10.67-5.5)·(10.67-5.5)·(10.67-10.34)
=√10.67 · 5.17 · 5.17 · 0.33
=√94.11512979
= 9.701
hb =
2S
b
=
2 · 9.701
5.5
= 3.528