В треугольнике со сторонами: a = 3.00, b = 3.70, с = 3.80 высоты равны ha = 3.435, hb = 2.785, hc = 2.712
Ответ:
a=3.00
b=3.70
c=3.80
α°=47.13°
β°=64.64°
γ°=68.22°
S = 5.153
ha=3.435
hb=2.785
hc=2.712
P = 10.5
Решение:
Угол:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
3.702+3.802-3.002
2·3.70·3.80
)
= arccos(
13.69+14.44-9
28.12
)
= 47.13°
Периметр:
P = a + b + c
= 3.00 + 3.70 + 3.80
= 10.5
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√5.25·(5.25-3.00)·(5.25-3.70)·(5.25-3.80)
=√5.25 · 2.25 · 1.55 · 1.45
=√26.54859375
= 5.153
Высота :
ha =
2S
a
=
2 · 5.153
3.00
= 3.435
hb =
2S
b
=
2 · 5.153
3.70
= 2.785
hc =
2S
c
=
2 · 5.153
3.80
= 2.712
Угол:
β° = arcsin(
b
a
sin(α°))
= arcsin(
3.70
3.00
sin(47.13°))
= arcsin(1.233·0.7329)
= 64.64°
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
3.80
3.00
sin(47.13°))
= arcsin(1.267·0.7329)
= 68.22°