В треугольнике со сторонами: a = 2.8, b = 3.9, с = 4.1, углы равны α° = 40.88°, β° = 65.74°, γ° = 73.37°
Ответ:
a=2.8
b=3.9
c=4.1
α°=40.88°
β°=65.74°
γ°=73.37°
S = 5.232
ha=3.737
hb=2.683
hc=2.552
P = 10.8
Решение:
Угол:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
3.92+4.12-2.82
2·3.9·4.1
)
= arccos(
15.21+16.81-7.84
31.98
)
= 40.88°
Периметр:
P = a + b + c
= 2.8 + 3.9 + 4.1
= 10.8
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√5.4·(5.4-2.8)·(5.4-3.9)·(5.4-4.1)
=√5.4 · 2.6 · 1.5 · 1.3
=√27.378
= 5.232
Высота :
ha =
2S
a
=
2 · 5.232
2.8
= 3.737
hb =
2S
b
=
2 · 5.232
3.9
= 2.683
hc =
2S
c
=
2 · 5.232
4.1
= 2.552
Угол:
β° = arcsin(
b
a
sin(α°))
= arcsin(
3.9
2.8
sin(40.88°))
= arcsin(1.393·0.6545)
= 65.74°
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
4.1
2.8
sin(40.88°))
= arcsin(1.464·0.6545)
= 73.37°