В треугольнике со сторонами: a = 4.617, b = 5, с = 5, углы равны α° = 55°, β° = 62.52°, γ° = 62.52°
Ответ:
a=4.617
b=5
c=5
α°=55°
β°=62.52°
γ°=62.52°
S = 10.24
ha=4.436
hb=4.096
hc=4.096
P = 14.62
Решение:
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √52 + 52 - 2·5·5·cos(55°)
= √25 + 25 - 50·0.5736
= √21.32
= 4.617
Угол:
β° = arcsin(
b
a
sin(α°))
= arcsin(
5
4.617
sin(55°))
= arcsin(1.083·0.8192)
= 62.52°
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
5
4.617
sin(55°))
= arcsin(1.083·0.8192)
= 62.52°
Периметр:
P = a + b + c
= 4.617 + 5 + 5
= 14.62
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√7.309·(7.309-4.617)·(7.309-5)·(7.309-5)
=√7.309 · 2.692 · 2.309 · 2.309
=√104.90130314127
= 10.24
Высота :
ha =
2S
a
=
2 · 10.24
4.617
= 4.436
hb =
2S
b
=
2 · 10.24
5
= 4.096
hc =
2S
c
=
2 · 10.24
5
= 4.096