В треугольнике со сторонами: a = 3, b = 4.36, с = 5 высоты равны ha = 4.331, hb = 2.98, hc = 2.599
Ответ:
a=3
b=4.36
c=5
α°=36.59°
β°=60°
γ°=83.36°
S = 6.497
ha=4.331
hb=2.98
hc=2.599
P = 12.36
Решение:
Угол:
α° = arcsin(
a
b
sin(β°))
= arcsin(
3
4.36
sin(60°))
= arcsin(0.6881·0.866)
= 36.58°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
4.362+52-32
2·4.36·5
)
= arccos(
19.0096+25-9
43.6
)
= 36.59°
Угол:
γ° = arcsin(
c
b
sin(α°))
= arcsin(
5
4.36
sin(60°))
= arcsin(1.147·0.866)
= 83.36°
Периметр:
P = a + b + c
= 3 + 4.36 + 5
= 12.36
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√6.18·(6.18-3)·(6.18-4.36)·(6.18-5)
=√6.18 · 3.18 · 1.82 · 1.18
=√42.20549424
= 6.497
Высота :
ha =
2S
a
=
2 · 6.497
3
= 4.331
hb =
2S
b
=
2 · 6.497
4.36
= 2.98
hc =
2S
c
=
2 · 6.497
5
= 2.599