В треугольнике со сторонами: a = 0.3, b = 0.3, с = 0.3569, углы равны α° = 53.49°, β° = 53.5°, γ° = 73°
Ответ:
a=0.3
b=0.3
c=0.3569
α°=53.49°
β°=53.5°
γ°=73°
S = 0.04306
ha=0.2871
hb=0.2871
hc=0.2413
P = 0.9569
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √0.32 + 0.32 - 2·0.3·0.3·cos(73°)
= √0.09 + 0.09 - 0.18·0.2924
= √0.1274
= 0.3569
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
0.3
0.3569
sin(73°))
= arcsin(0.8406·0.9563)
= 53.5°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
0.32+0.35692-0.32
2·0.3·0.3569
)
= arccos(
0.09+0.12737761-0.09
0.2141
)
= 53.49°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
0.3
0.3569
sin(73°))
= arcsin(0.8406·0.9563)
= 53.5°
Периметр:
P = a + b + c
= 0.3 + 0.3 + 0.3569
= 0.9569
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√0.4785·(0.4785-0.3)·(0.4785-0.3)·(0.4785-0.3569)
=√0.4785 · 0.1785 · 0.1785 · 0.1216
=√0.0018539241336
= 0.04306
Высота :
ha =
2S
a
=
2 · 0.04306
0.3
= 0.2871
hb =
2S
b
=
2 · 0.04306
0.3
= 0.2871
hc =
2S
c
=
2 · 0.04306
0.3569
= 0.2413