В треугольнике со сторонами: a = 4.2, b = 3.1, с = 2.8, углы равны α° = 90.63°, β° = 47.56°, γ° = 41.81°
Ответ:
a=4.2
b=3.1
c=2.8
α°=90.63°
β°=47.56°
γ°=41.81°
S = 4.34
ha=2.067
hb=2.8
hc=3.1
P = 10.1
Решение:
Угол:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
3.12+2.82-4.22
2·3.1·2.8
)
= arccos(
9.61+7.84-17.64
17.36
)
= 90.63°
Периметр:
P = a + b + c
= 4.2 + 3.1 + 2.8
= 10.1
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√5.05·(5.05-4.2)·(5.05-3.1)·(5.05-2.8)
=√5.05 · 0.85 · 1.95 · 2.25
=√18.83334375
= 4.34
Высота :
ha =
2S
a
=
2 · 4.34
4.2
= 2.067
hb =
2S
b
=
2 · 4.34
3.1
= 2.8
hc =
2S
c
=
2 · 4.34
2.8
= 3.1
Угол:
β° = arcsin(
b
a
sin(α°))
= arcsin(
3.1
4.2
sin(90.63°))
= arcsin(0.7381·0.9999)
= 47.56°
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
2.8
4.2
sin(90.63°))
= arcsin(0.6667·0.9999)
= 41.81°