В треугольнике со сторонами: a = 12.49, b = 10, с = 14, углы равны α° = 60°, β° = 43.89°, γ° = 76.12°
Ответ:
a=12.49
b=10
c=14
α°=60°
β°=43.89°
γ°=76.12°
S = 60.71
ha=9.721
hb=12.14
hc=8.673
P = 36.49
Решение:
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √102 + 142 - 2·10·14·cos(60°)
= √100 + 196 - 280·0.5
= √156
= 12.49
Угол:
β° = arcsin(
b
a
sin(α°))
= arcsin(
10
12.49
sin(60°))
= arcsin(0.8006·0.866)
= 43.89°
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
14
12.49
sin(60°))
= arcsin(1.121·0.866)
= 76.12°
Периметр:
P = a + b + c
= 12.49 + 10 + 14
= 36.49
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√18.25·(18.25-12.49)·(18.25-10)·(18.25-14)
=√18.25 · 5.76 · 8.25 · 4.25
=√3685.77
= 60.71
Высота :
ha =
2S
a
=
2 · 60.71
12.49
= 9.721
hb =
2S
b
=
2 · 60.71
10
= 12.14
hc =
2S
c
=
2 · 60.71
14
= 8.673