В треугольнике со сторонами: a = 12, b = 8.065, с = 5.799, углы равны α° = 119°, β° = 36°, γ° = 25°
Ответ:
a=12
b=8.065
c=5.799
α°=119°
β°=36°
γ°=25°
S = 20.42
ha=3.403
hb=5.064
hc=7.054
P = 25.86
Решение:
Сторона:
b = a·
sin(β°)
sin(α°)
= 12·
sin(36°)
sin(119°)
= 12·
0.5878
0.8746
= 12·0.6721
= 8.065
Угол:
γ° = 180 - α° - β°
= 180 - 119° - 36°
= 25°
Высота :
hc = a·sin(β°)
= 12·sin(36°)
= 12·0.5878
= 7.054
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √122 + 8.0652 - 2·12·8.065·cos(25°)
= √144 + 65.04 - 193.56·0.9063
= √33.62
= 5.798
или:
c = a·
sin(γ°)
sin(α°)
= 12·
sin(25°)
sin(119°)
= 12·
0.4226
0.8746
= 12·0.4832
= 5.798
или:
c = b·
sin(γ°)
sin(β°)
= 8.065·
sin(25°)
sin(36°)
= 8.065·
0.4226
0.5878
= 8.065·0.719
= 5.799
Периметр:
P = a + b + c
= 12 + 8.065 + 5.799
= 25.86
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√12.93·(12.93-12)·(12.93-8.065)·(12.93-5.799)
=√12.93 · 0.93 · 4.865 · 7.131
=√417.1716186435
= 20.42
Высота :
ha =
2S
a
=
2 · 20.42
12
= 3.403
hb =
2S
b
=
2 · 20.42
8.065
= 5.064