В треугольнике со сторонами: a = 96.2, b = 49.18, с = 93.54, углы равны α° = 78°, β° = 30°, γ° = 72°
Ответ:
a=96.2
b=49.18
c=93.54
α°=78°
β°=30°
γ°=72°
S = 2249.8
ha=46.77
hb=91.49
hc=48.1
P = 238.92
Решение:
Сторона:
a = b·
sin(α°)
sin(β°)
= 49.18·
sin(78°)
sin(30°)
= 49.18·
0.9781
0.5
= 49.18·1.956
= 96.2
Угол:
γ° = 180 - α° - β°
= 180 - 78° - 30°
= 72°
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √96.22 + 49.182 - 2·96.2·49.18·cos(72°)
= √9254.4 + 2418.7 - 9462.2·0.309
= √8749.3
= 93.54
или:
c = a·
sin(γ°)
sin(α°)
= 96.2·
sin(72°)
sin(78°)
= 96.2·
0.9511
0.9781
= 96.2·0.9724
= 93.54
или:
c = b·
sin(γ°)
sin(β°)
= 49.18·
sin(72°)
sin(30°)
= 49.18·
0.9511
0.5
= 49.18·1.902
= 93.54
Высота :
hc = a·sin(β°)
= 96.2·sin(30°)
= 96.2·0.5
= 48.1
Периметр:
P = a + b + c
= 96.2 + 49.18 + 93.54
= 238.92
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√119.46·(119.46-96.2)·(119.46-49.18)·(119.46-93.54)
=√119.46 · 23.26 · 70.28 · 25.92
=√5061729.945001
= 2249.8
Высота :
ha =
2S
a
=
2 · 2249.8
96.2
= 46.77
hb =
2S
b
=
2 · 2249.8
49.18
= 91.49