В треугольнике со сторонами: a = 3714.5, b = 4535, с = 3015, углы равны α° = 54.56°, β° = 84.04°, γ° = 41.4°
Ответ:
a=3714.5
b=4535
c=3015
α°=54.56°
β°=84.04°
γ°=41.4°
S = 5569728
ha=2998.9
hb=2456.3
hc=3694.7
P = 11264.5
Решение:
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
4535
3015
sin(41.4°))
= arcsin(1.504·0.6613)
= 84.04°
Угол:
α° = 180 - γ° - β°
= 180 - 41.4° - 84.04°
= 54.56°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √45352 + 30152 - 2·4535·3015·cos(54.56°)
= √20566225 + 9090225 - 27346050·0.5799
= √13798476
= 3714.6
или:
a = b·
sin(α°)
sin(β°)
= 4535·
sin(54.56°)
sin(84.04°)
= 4535·
0.8147
0.9946
= 4535·0.8191
= 3714.6
или:
a = c·
sin(α°)
sin(γ°)
= 3015·
sin(54.56°)
sin(41.4°)
= 3015·
0.8147
0.6613
= 3015·1.232
= 3714.5
Периметр:
P = a + b + c
= 3714.5 + 4535 + 3015
= 11264.5
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√5632.3·(5632.3-3714.5)·(5632.3-4535)·(5632.3-3015)
=√5632.3 · 1917.8 · 1097.3 · 2617.3
=√31021870300028
= 5569728
Высота :
ha =
2S
a
=
2 · 5569728
3714.5
= 2998.9
hb =
2S
b
=
2 · 5569728
4535
= 2456.3
hc =
2S
c
=
2 · 5569728
3015
= 3694.7