В треугольнике со сторонами: a = 6.068, b = 6, с = 7, углы равны α° = 55°, β° = 54.1°, γ° = 70.97°
Ответ:
a=6.068
b=6
c=7
α°=55°
β°=54.1°
γ°=70.97°
S = 17.2
ha=5.669
hb=5.733
hc=4.914
P = 19.07
Решение:
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √62 + 72 - 2·6·7·cos(55°)
= √36 + 49 - 84·0.5736
= √36.82
= 6.068
Угол:
β° = arcsin(
b
a
sin(α°))
= arcsin(
6
6.068
sin(55°))
= arcsin(0.9888·0.8192)
= 54.1°
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
7
6.068
sin(55°))
= arcsin(1.154·0.8192)
= 70.97°
Периметр:
P = a + b + c
= 6.068 + 6 + 7
= 19.07
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√9.534·(9.534-6.068)·(9.534-6)·(9.534-7)
=√9.534 · 3.466 · 3.534 · 2.534
=√295.92173301566
= 17.2
Высота :
ha =
2S
a
=
2 · 17.2
6.068
= 5.669
hb =
2S
b
=
2 · 17.2
6
= 5.733
hc =
2S
c
=
2 · 17.2
7
= 4.914