В треугольнике со сторонами: a = 4, b = 4, с = 2.5 высоты равны ha = 2.375, hb = 2.375, hc = 3.8
Ответ:
a=4
b=4
c=2.5
α°=71.79°
β°=71.79°
γ°=36.42°
S = 4.75
ha=2.375
hb=2.375
hc=3.8
P = 10.5
Решение:
Угол:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
42+2.52-42
2·4·2.5
)
= arccos(
16+6.25-16
20
)
= 71.79°
Периметр:
P = a + b + c
= 4 + 4 + 2.5
= 10.5
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√5.25·(5.25-4)·(5.25-4)·(5.25-2.5)
=√5.25 · 1.25 · 1.25 · 2.75
=√22.55859375
= 4.75
Высота :
ha =
2S
a
=
2 · 4.75
4
= 2.375
hb =
2S
b
=
2 · 4.75
4
= 2.375
hc =
2S
c
=
2 · 4.75
2.5
= 3.8
Угол:
β° = arcsin(
b
a
sin(α°))
= arcsin(
4
4
sin(71.79°))
= arcsin(1·0.9499)
= 71.79°
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
2.5
4
sin(71.79°))
= arcsin(0.625·0.9499)
= 36.42°