В треугольнике со сторонами: a = 73.36, b = 37.25, с = 70, углы равны α° = 80°, β° = 30°, γ° = 70°
Ответ:
a=73.36
b=37.25
c=70
α°=80°
β°=30°
γ°=70°
S = 1284.4
ha=35.02
hb=68.96
hc=36.7
P = 180.61
Решение:
Угол:
γ° = 180 - α° - β°
= 180 - 80° - 30°
= 70°
Сторона:
a = c·
sin(α°)
sin(γ°)
= 70·
sin(80°)
sin(70°)
= 70·
0.9848
0.9397
= 70·1.048
= 73.36
Сторона:
b = c·
sin(β°)
sin(γ°)
= 70·
sin(30°)
sin(70°)
= 70·
0.5
0.9397
= 70·0.5321
= 37.25
Периметр:
P = a + b + c
= 73.36 + 37.25 + 70
= 180.61
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√90.31·(90.31-73.36)·(90.31-37.25)·(90.31-70)
=√90.31 · 16.95 · 53.06 · 20.31
=√1649615.4438687
= 1284.4
Высота :
ha =
2S
a
=
2 · 1284.4
73.36
= 35.02
hb =
2S
b
=
2 · 1284.4
37.25
= 68.96
hc =
2S
c
=
2 · 1284.4
70
= 36.7