В треугольнике со сторонами: a = 1.501, b = 0.5002, с = 2 высоты равны ha = 0.05163, hb = 0.1549, hc = 0.03875
Ответ:
a=1.501
b=0.5002
c=2
α°=3°
β°=1°
γ°=176°
S = 0.03875
ha=0.05163
hb=0.1549
hc=0.03875
P = 4.001
Решение:
Угол:
γ° = 180 - α° - β°
= 180 - 3° - 1°
= 176°
Сторона:
a = c·
sin(α°)
sin(γ°)
= 2·
sin(3°)
sin(176°)
= 2·
0.05234
0.06976
= 2·0.7503
= 1.501
Сторона:
b = c·
sin(β°)
sin(γ°)
= 2·
sin(1°)
sin(176°)
= 2·
0.01745
0.06976
= 2·0.2501
= 0.5002
Периметр:
P = a + b + c
= 1.501 + 0.5002 + 2
= 4.001
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√2.001·(2.001-1.501)·(2.001-0.5002)·(2.001-2)
=√2.001 · 0.5 · 1.5008 · 0.00099999999999989
=√0.0015015503999998
= 0.03875
Высота :
ha =
2S
a
=
2 · 0.03875
1.501
= 0.05163
hb =
2S
b
=
2 · 0.03875
0.5002
= 0.1549
hc =
2S
c
=
2 · 0.03875
2
= 0.03875