В треугольнике со сторонами: a = 0.28, b = 0.28, с = 0.3332, углы равны α° = 53.49°, β° = 53.47°, γ° = 73°
Ответ:
a=0.28
b=0.28
c=0.3332
α°=53.49°
β°=53.47°
γ°=73°
S = 0.03749
ha=0.2678
hb=0.2678
hc=0.225
P = 0.8932
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √0.282 + 0.282 - 2·0.28·0.28·cos(73°)
= √0.0784 + 0.0784 - 0.1568·0.2924
= √0.111
= 0.3332
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
0.28
0.3332
sin(73°))
= arcsin(0.8403·0.9563)
= 53.47°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
0.282+0.33322-0.282
2·0.28·0.3332
)
= arccos(
0.0784+0.11102224-0.0784
0.1866
)
= 53.49°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
0.28
0.3332
sin(73°))
= arcsin(0.8403·0.9563)
= 53.47°
Периметр:
P = a + b + c
= 0.28 + 0.28 + 0.3332
= 0.8932
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√0.4466·(0.4466-0.28)·(0.4466-0.28)·(0.4466-0.3332)
=√0.4466 · 0.1666 · 0.1666 · 0.1134
=√0.0014056647930864
= 0.03749
Высота :
ha =
2S
a
=
2 · 0.03749
0.28
= 0.2678
hb =
2S
b
=
2 · 0.03749
0.28
= 0.2678
hc =
2S
c
=
2 · 0.03749
0.3332
= 0.225